Ironically, I'm about to knock the Big Three and Rhydon down a notch. Not by outclassing them, but by introducing a meta assassin whose whole job is to beat them. So with that in mind...
This just in, breaking news: Local area ape literally too angry to die.
Pokemon: Annihilape
Stats: 110/115/80/70/90 [BST:465/535] (Special is average of Special Attack and Special Defense from Gen 9)
Typing: Ghost/Fighting
Movepool: Primeape's moveset + Earthquake (Note: Primeape doesn't get Earthquake until Gen 3. Thus it doesn't have it in this metagame).
Description: Ghost and Fighting are nominally two of the worst types in the game. The former, due to having no good moves, and the latter, due to being weak to Psychic, the second-best type in the game. However, Annihilape makes these two typings work together in a way that truly lets both shine, by being the single best Pokemon ever at rolling the faces of Tauros, Chansey, Snorlax and Rhydon. Their STAB completely fails against Annihilape's Ghost-typing, and even if you stick with Low Kick, Annihilape will still on average beat any member of the big three in a damage race (It's somewhat close against Tauros and Snorlax, but Chansey stands no chance outside of a lucky Ice Beam freeze). It can also leave a dent in other threats through coverage moves like the Elemental Punches, but really, if you're using Annihilape, it's because you hate the bull, blob and... bear? whatever the hell Snorlax is supposed to be.
Regardless, Annihilape also has very clear weaknesses- or one in particular anyway. Due to the way Gen 1 is coded, Annihilape has to flee screaming at the sight of any incoming Psychic-type, given how its stabs are similarly ineffective against Psychics, and it doesn't fare too well against 'mons like Zapdos either.
Also resubbing this one:
Pokemon: Latias
Stats: 70/70/80/120/110 [BST: 450/570.] (Special is the average of Latias' special stats from later gens. HP and physical stats are reduced by 10)
Typing: Dragon/Psychic
Movepool: Blizzard, Thunderbolt, Psychic, Recover, Light Screen, Reflect, Toxic, Conversion, Earthquake, Double Team, Hyper Beam, Ice Beam, Thunder, Mimic, Earthquake, Rest, Roar, Strength, Substitute, Dragon Rage, Growl, Agility, Bide, Rage, Thunder Wave, Mist Ball, Draco Meteor, Conversion, Growl, Universals, Draco Meteor
Description: Latias can be considered a slower alternative to Alakazam, but a much bulkier one, not to mention one with a usable physical movepool. Latias' Dragon-typing is also a double-edged sword: while Latias does gain some nice resistances to Water, Grass and Electric, she also gains a crippling Ice weakness, which can hinder her in comparison to Alakazam when faced with the Blizzards that tend to fly around everywhere. What Latias does have going for her is a wide, varied movepool that lets her generally threaten more of the metagame than Alakazam: Thunderbolt mauls Slowbro and Starmie, Blizzard hamstrings Dragonite and opposing Latias (as well as Aerodactyl, Beedrill and Zapdos), Surf dumpsters the rocks, Psychic is Psychic, Draco Meteor is a horrendously powerful neutral hit on everything (except for opposing Dragon-types, who get obliterated by it), and so on. She even gets access to some physical moves like Earthquake, just in case Chansey got any funny ideas about trying to wall her, though Latias can't really handle Snorlax very well. She can, however, also run a nasty defensive set with Recover, Light Screen, Reflect, and Toxic, and even potentially make usage of the rare Conversion to alter her type, in case it wants to take advantage of its auxillary options and alter her weaknesses. It certainly has the bulk to make usage of the move, unlike Porygon. Latias' main issue is not doing much of note to Snorlax, and Tauros is a risky matchup for her (though it is also a risky matchup for the Tauros, as the two speed tie, and Tauros does not appreciate eating a possible Special drop from Psychic/Mist Ball or a freeze from Blizzard).
And just to come full circle I'll resub the very first one I made too:
Pokemon: Charizard
Stats: 70/100/70/109/100 [BST: 449/558] (Special is now Charizard's Special Attack from later gens. Attack has been boosted to base 100, 4 points below Mega Charizard Y's base 104. Reduced HP and Defense slightly).
Typing: Fire/Flying
Movepool Changes: +Thunder Punch (Can you believe Charizard doesn't actually get it in Gen 2?)
Description: To differentiate itself from the notably bulkier and far more specially powerful Moltres, Charizard gets an Anti-water coverage option in Thunder Punch (taken from later generations) and gains an increase to its attack from its Mega Y form (Megazard Y does actually have higher attack than base Charizard). This affords Charizard a unique niche over Moltres, in that Charizard can threaten targets on both sides of the attacking spectrum- in a way, reflective of the duality of Charizard's Mega Evolutions from Gen 6. The higher attack makes Charizard actually able to leave a dent in Rhydon and Golem, or even threaten to take them out if it manages to set a Swords Dance up before they switch in, while the higher special attack means even the Mighty Tauros is not a safe switch-in, almost always being 2HKO'd by Fire Blast. With that being said, Charizard is stuffed by Slowbro, as even Thunder Punch does a measly 34-40% even before Slowbro gets an Amnesia up, while Charizard's considerable special does not protect it from having a high chance of being 2HKO'd by Surf, making using Charizard carelessly an extremely bad idea. Starmie is also an incredibly bad matchup for Charizard, as Charizard still cannot 2HKO even with Thunder Punch without a crit, and will likely eat Thunder Wave paralysis as a result, crippling the main thing that makes Charizard so deadly: its speed. Ultimately, the main thing that simultaneously makes Charizard so difficult to check, also gives it an issue: It suffers from 4MSS, believe it or not. It wants all of Fire Blast, Blast Burn, Earthquake, Hyper Beam, Swords Dance, Thunder Punch and Slash, but it can only fit 4 of these at once. If it lacks Earthquake, it can't do anything to Rhydon/Golem. If it lacks Thunder Punch, Slowbro and Starmie kill it with ease. No Fire Blast means Tauros and Zapdos maul you. Blast Burn hits even harder than Fire Blast, it needs Swords Dance alongside EQ to actually beat the rocks, Slash is nice for pesky defense boosters like Reflect Alakazam and Chansey, and Hyper Beam is Hyper Beam. It does lose a tiny bit of bulk, though, to further emphasise the "fast and deadly, but frail" spread it is supposed to have in comparison to its brethren Venusaur and Blastoise.
In a few ways, this updated Charizard could be considered a hybrid of Tauros and Moltres, featuring advantages and disadvantages compared to the points of reference. Compared to Tauros, Charizard has a higher Special and access to Slash and Swords Dance, but it's slower, lacks STAB on Normal moves, mandating setup for physical builds compared to Tauros who's threatening right out of the gate (to say nothing about the fact that, since this is Gen 1, Pure Normal is a
much better typing than Fire/Flying) and has much worse physical bulk. Compared to Moltres, Charizard's Special is lower and it's frailer, but it makes up for it with higher speed and attack, a usable physical movepool, and the crucial additional coverage that Thunder Punch provides, allowing Charizard to at least dent the Water-types that would otherwise give Moltres no end of trouble.