No trainer rematches! Ugh!
Also, I'm really bummed by the lack of Fairy Pokémon. I thought a lot of Pokémon that fit the Fairy-type flavor-wise got miffed by Game Freak. Like Uxie/Azelf/Mesprit (which are literally fairies), Misdreavus (based off a banshee, which is one of the Fair Folk. Mawile was re-typed to Fairy because it was based off one of the Fair Folk), Celebi (possibly based off a sprite or fairy), Cresselia (has enough connections to the moon), Jirachi (maybe a stretch, but it does grant wishes, so it'd fit right in the world of Fairly Odd Parents) and so on. But that's just me. Sad thing is, a lot of these Pokémon would be a lot better competitively with a Fairy typing (especially Jirachi!)
I daresay no, actually.
From Team Aqua/Magma on, all evil teams have been thorougly stupid, wanting to destroy the world for really contrived reasons. It mostly comes down to the hubris of their leader, who somehow tricks a bunch of grunts into following his plan. Said grunts follow the plan without questioning it, idiotically believing that "Team [name] will take over the world!" and that participation in the plan will somehow save them all from the destruction. They also dress in silly costumes, and serve more as comic relief than a legitimate threat.
And of course, the world as we know it is always at stake. This gets really boring after a while. It's always: "Save the world, 10-year-old, because nobody else bother to!". For being a threat to the world, surely the most powerful trainers around take the evil teams lightly. And true enough, the evil organization plotting to destroying/taking over the world is easily beaten by the 10-year-old. That gives me an impression that their plans weren't thought out at all, greatly diminishing the sensation of the world being threatened. In short, the evil teams from RSE on have been a bunch of weirdly-dressing doofuses who bite over way more than they could possibly hope to chew, with no consideration or no backup plan whatsoever.
Contrast Team Rocket, who, while having way smaller ambitions, also achieved the greatest success of all the evil teams.
Firstly, Team Rocket practically owned the region at the start of the game. Team Rocket members were bullying people and stealing Pokémon in every city in the region, save for Pallet Town and Pewter City (and maybe Fuchsia, I can't really remember). They weren't some fringe terrorist organization with greater ambitions than brains, they were the freakin' mafia. Their casino in Celadon raked in money for their organization, while also providing them with a hiding spot. Even though their lair on Cinnabar Island burned down, they succeeded in their plans there, creating Mewtwo (and subsequently losing control of it, but oh well, not really much they could do to stop that, and the player character had zero interference in that plan). The police were powerless to stop them, and Team Rocket managed to seize control of the headquarters of the greatest corporation in Kanto, stealing their technology.
And the grunts? Instead of brainwashed nobodies tricked into following a plan to the end of the world, they willingly joined for money and power. Team Rocket members, freely strolling the streets of Kanto in uniform, were openly bragging about their membership. Meanwhile, the name of the organization was only whispered by others, fearing the iron grip they held on Kanto. At the start of the game, Team Rocket might have been the single most powerful organization in Kanto, nobody opposing them but this one, idealist, talented trainer from Pallet Town. They were at the top of the game, having even infiltrated the Pokémon League (with Giovanni being an official Gym Leader), they were making butt-loads of money, and successfully stole all the Pokémon they wanted. And that was it. They didn't feel like needlessly destroying the world. Kanto was theirs already, they had got everything they wanted. They felt like a powerful enemy, because they were powerful. And instead of beating their leaders in silly outfits, you went from town to town in Kanto, beating back Team Rocket grunts, loosening their grasp on Kanto until you managed to convince their leader to give up and live a crime-free life. He then walks away, unscathed and unpunished. As a ten-year-old, you might convince him to disband the organization, but you have no way of giving him his deserved punishment, or making him speak for his crimes in court. Truly, Giovanni didn't fall from power, he simply stepped down and walked away a free man.
As for the legendary Pokémon, they stayed legendary. Zapdos, Moltres and Articuno were hidden in the most remote corners of the region, outside Team Rocket's sphere of influence, and outside their plans at all, for that matter. What could Team Rocket hope to achieve with them, anyway? They had the region at their fingertips already, no need to bother with a few ultra-rare birds hanging around in the middle of nowhere. Team Rocket didn't need any Legendaries to achieve their goal. Their goal was money and power, and they already had it all when you started your adventure.
TL;DR: Instead of simply observing an evil team trying to destroy the world (and being totally unable to influence it, apart from causing them to fail at the last minute), RBY had you face a powerful organization and actively bring them down from power. Team Rocket were way more badass than all the rest of the evil teams combined.
I disagree. You're fallaciously writing off all the non-Rocket teams to try and make a point and there are a couple of inaccuracies in your post. You make it sound like pretty much every villainous team just wanted to summon a legendary and destroy the world, which is not really being fair to them.
The members of team Aqua and Magma, while both being really stupid, all genuinely thought they were improving the world. While they definitely were idiots for dicking around with powerful forces they couldn't really control, they weren't actively trying to destroy or take over the world. In Ruby, Team Aqua are more-or-less portrayed as good guys (same for Team Magma in Sapphire)
A lot of Team Galactic members were completely unaware of the full extent of Cyrus' plans. Some of them really bought Team Galactic's facade of researching cleaner sources of energy. Keep in mind Cyrus was a lying, manipulative dickbag. (Best shown by his speech to Team Galactic at their HQ in Platinum) Nobody knew that he planned his new world solely for himself. The members of Team Galactic who knew about Cyrus' plan thought he would create a world tailored for them.
On the surface Team Plasma never wanted to take over the world. They did want to completely change society as we knew it, but that's still hardly "destroying/take over the world". In Black and White, everybody in Team Plasma except Ghetsis + Sages wanted to release Pokémon because they thought Pokémon were mistreated in human society. The figurehead leader N was genuinely devoted to this cause. Misguided as he was, he did get one of Unova's deities on his side, so he's not exactly loony. Given his abusive, neglectful upbringing he can't really be blamed for his views. Also keep in mind the authorities do play a role in this game (Bianca rallies together the Gym Leaders to help fight off Team Plasma, The Champion tries to defeat N but loses, the Elite Four were forbidden to interfere on Alder's orders but probably would have lost against N anyway; the fact the Black and White actually shows the Pokémon League interfering against Team Plasma is part of why I think so highly of it.) Also, Team Plasma managed to hack into the Pokémon Center's PC system and would have released all the Pokémon inside once N defeated the player character, which would have been a huge step toward their goals. They were hardly ineffectual. Again, keep in mind the only people who openly planned to rule Unova were Ghetsis and the Sages, and Ghetsis was a manipulative dickbag - right from the time N was born, he took advantage of N's powers, crafting N into his own tool to release Pokémon. (Ironically, Ghetsis being a completely terrible father makes him pretty similar to Giovanni)
Team Plasma in Black 2 and White 2 pretty openly wanted to rule the country. Arguably, Team Plasma from B2W2 is pretty similar to Team Rocket, since they're in a direct pursuit of power, just more overt about it. I'm surprised you just overlooked this similarity. The members of Team Plasma in B2W2 know exactly what they're signing up for: power. Also, as another user mentioned, the organization nuked a whole city with a freeze ray. If that doesn't show they mean business, what does?
I'll give Team Flare as being straightforward in wanting to eliminate everybody besides themselves. But they had good defenses. One of the Kalos Elite Four is a member of Team Flare, and a newscaster, so Team Flare also had somebody in the Pokémon League, and the media. Lysandre was concerned about preserving the resources of the world, so if anything he seems like a well-intentioned extremist, just gone to an un-salvageable extreme.
About Team Rocket: while they were responsible for creating Mewtwo in the anime, this isn't so for the games. There's nothing linking Dr. Fuji/Mr. Fuji and the scientists who created Mewtwo to Team Rocket. Keep in mind Fuji actually stands up to Team Rocket for their cruelty towards Pokémon and they hold him hostage until the player character rescues him. Also, if we take the Celebi event from HeartGold and SoulSilver into account, Giovanni never did give up his life of crime. And he's hardly the only one to get off scot-free. Ghetsis was basically a complete monster (let's see, he's an abusive father, froze a city, and we see that he basically loves breaking other people's spirits) and he basically got off scot-free, other than being a broken man himself by the end of B2W2.
Also, plenty of games had authority figures trying to deal with the local crisis: Lance in G/S/C/HG/SS, Steven in R/S/E and Wallace in Emerald, Cynthia, and Looker from the International Police in Platinum, pretty much the whole Pokémon League in Black and White, and Cheren in Black 2 and White 2. A lot of them are pretty ineffectual. I'll admit Game Freak is really inconsistent with this but they kind of make an effort...
For me personally, Team Rocket has always been kind of boring... It's kind of hard to see them as more than just unambitious thugs. One thing I like about the later games is the ambition of all the leaders... all the leaders are charming, manipulative bastards (except N) who use underlings very well to get what they want. I think it's worth nothing that every new region from Diamond/Pearl onwards (including Hoenn in Omega Ruby and Alpha Sapphire) focuses on the mythology of those regions... the box Legendaries (Kyogre and Groudon to some extent, Dialga, Palkia, Zekrom, Reshiram, and Xerneas and Yveltal to some extent) are basically deities to the people of their respective regions... considering that the later villanious are somewhat like cults (to a small extent), it makes sense that the leaders try to invoke these deities to get their way, even if these guys do tend to dick around with forces they can't control. I also found Ghetsis and Cyrus much more interesting than anything in Team Rocket, in part of because of their amazing skills as manipulative dickbags. Cyrus' morivations, and Team Plasma's fake motivations, really made you think, I think. I'll give Pokémon Origins points for trying to do
something interesting, character-wise, with Giovanni. But I digress.
TL;DR - While all the villanous teams would change or eradicate society as we know it, they hardly all planned to destroy/take over the world. A lot of the members of villanous teams, including N, Archie and Maxie (and Lysandre, on some level) had good intentions, despite being misguided. Please don't lump together all of the villainous teams to make an (inaccurate) point, and please don't romanticize Team Rocket. 
