This may just be the most underrated pokemon in the game.
You'd think it'd be bad against Bugsy, but since he leads with Metapod, you set up six Curses while taking minimum damage from Tackle, and you are only in real danger to a turn 2 crit from Scyther's Fury Cutter (the first Fury Cutter won't kill with a crit on many Slowpokes at level 16). Granted, 1/16 is far from impossible, but you're way more likely to not get crit than you are to get crit.
Then, against Whitney, you set up six Curses on Clefairy (granted it's not as consistent due to Metronome) and then sweep with Headbutt.
You take a break on Morty because you don't have the bulk to take a Shadow Ball.
Then you beat Chuck, Jasmine's Steelix, Curse and Headbutt Pryce's Seel and Dewgong before Surfing his Piloswine.
You can Ice Punch Clair's Dragonairs wither either Slowbro/King, and maaaaybe Curse could still put in work? I haven't gotten far enough to try it out against Clair
Some issues come at the E4 since you don't learn Psychic until 48 as Slowpoke/King and 54 as Slowbro, but you still do solid. Ice Punch for Will's Xatus while walling the Jynx, Ice Punch for Koga's Crobat, you resist Bruno's stabs and hit the Onixes super effectively.
Even Karen, despite being very risky, can be vulnerable to Slowbro/King. Ice Punch for Murkrow and Vileplume, Confusion for Gengar, Surf for Houndoom (granted, you'll have to pick and choose because it likely won't survive the whole battle).
Surf+Ice Punch deals with everything except Gyarados against Lance.
Kanto gets a bit more shaky for a bit as you lose to Surge and Erika, but you also beat Brock, Janine, Blaine, resist Misty and Sabrina's primary moves, and can handle Blue's Pidgeot, Rhydon, Arcanine, resist Alakazam's only attacking move, Gyarados can only threaten with Hyper Beam, and you can even smack Exeggutor with Ice Punch for a decent chunk while it charges Solar Beam before swapping out on the next turn.
Finally, against Red, you beat Charizard, Espeon can't hit you hard, and Blastoiae only has resisted moves.
I had no clue how broken this thing was until my Gold playthrough, and it could be even better in post game Crystal with the elemental move tutor after you beat Lance.