Might as well give my input on this. Again.
I'm pretty sure I had the most successful Rain Dance team in the period of time when we were discussing banning Damp Rock. It peaked at a CRE of 1669, which is fairly low compared to my other CRE peaks (1782 with "standard" bulky offense last metagame), but which is still in the top percentile of the ladder. So hopefully my credibility as far as my understanding of Rain Dance is established in this discussion, for those of you who don't really know me that well.
I specifically mention that because a very common argument against players who advocated a Damp Rock ban was "you never played any good players" or "it's easy to win against teams without rain checks". Regardless of your opinion of the quality of play on the ladder, it is difficult to argue that I got that high without facing, and beating, multiple players who had solid teams and a good understanding of how to play against rain.
Now that we've established that, I'll explain the mechanism behind my team, why it was so successful, and why I ultimately stopped using it.
My Rain Dance team relied on Spikes support from a bulky Qwilfish lead. This was during the Froslass metagame, so that lead was very rare at the time; I used it because it had very high speed (in the rain), good bulk, access to Spikes and Explosion, and good matchups against common leads. Spikes support was one of the many things that differentiated my team from standard rain teams, and it made a huge difference; one layer of spikes support and stealth rock enabled Specs Gorebyss to do silly shit like 2hko Chansey and Milotic 100% of the time with Hydro Pump. It was fully possible to muscle my way through the standard teams at the time with just Gorebyss, which is what resulted in the massive Water Absorber spike (note: at this time Toxicroak was somewhere around 29th in usage, possibly lower). Once that happened, and once people started abusing Raikou and Moltres with more and more frequency (both of which gave rain teams insane trouble) I decided to switch up my team. I kept the Qwilfish lead, but I switched up my rain supporters; I went from Uxie to physical Mespirit, who could break Raikou/Moltres/Mismagius subs, and went from Toxicroak to Lanturn, who could set up Rain against Raikou and Moltres. I also replaced Specs on Gorebyss with Life Orb now that it could no longer 2hko the metagame with one move, and switched from special Ludicolo to physical Ludicolo, which is arguably much more threatening. This is the incarnation of my team that most people remember, especially my Healing Wish shenanigans with Mespirit and Heal Bell hijinks with Lanturn. It was extremely successful, particularly due to my playstyle, and only encountered difficulty against teams that, literally, had at least 5 rain checks...or if I was playing terribly, which could sometimes be the case due to how boring Rain is. Anyway, Tangrowth started gaining popularity at this time as one of the few things that could tank Kabutops while still being useful against other Pokemon, and stall became even more common (stall was the only playstyle that could handle Raikou so it was already fairly common).
The rising popularity of rain checks and the tendency to carry multiple of this in a team, particularly on a stall team, really reduced the impact of rain. It's also very difficult for rain to adapt to these metagame trends because of how one-dimensional the playstyle is; I couldn't do a damn thing about all the Tangrowth/Hitmontop/Milotic/Chansey/Registeel/Omastar teams. This, combined with how boring rain dance was in general, resulted in a lot of players abandoning the playstyle until the Damp Rock vote got that "meh" reception at the very end. It has nothing to do with how broken rain is, because it is certainly very broken. I could, if I were so inclined, start another rain frenzy (I want to make an alt called WhaleBlitz anyway, this would be relevant). But the ultimate problem with rain is that it cannot deal with metagame centralizations, unlike other broken Pokemon. Raikou could switch between SubCM, Shuca, RestTalk, etc. to beat various trends in its counters. Mence could switch from the mixed set to the DD set at any time. Cresselia could run any number of sets that fuck over entirely different sets of would-be counters. Even with addition of random Psychic moves for Toxicroak, Rain is very inflexible, and that is ultimately what resulted in people deeming it "balanced".
Ultimately it comes down to whether you believe an overwhelming playstyle that can easily be adapted to is broken or not. Basically, against a rain player of equal skill, whether you win or lose is determined as soon as the match starts, by the team-matchup.
And regardless of what people may think, "standard" teams these days do a very poor job against Rain. Toxicroak, Milotic, and Venusaur are indeed great Pokemon...but a single Kabutops or Ludicolo beats all of them, easily. It requires the level of centralization there was back during Lass/Raikou meta, a level of centralization which coincidentally was also appropriate towards non-rain teams at the time, in order to have a solid chance of beating rain dance teams. Or it requires that the player be more skilled than the rain user, which is currently what I'm relying on now against the rare rain dance team (although bad predictions still utterly fuck me from time to time...)
tldr read the fucking post you lazy bitches it's informative and took me a while to type out