When getting caught up in the nostalgia, its easy to forget how much the Gen 2 pokemon sucked during Gen 2.

Typhlosion: Stuck with Ember until level 31, then doesn't get Flamethrower until level 60.

Heracross: you'd think this bug/fighting hybrid would be great for taking down Whitney's Miltank, the Steelix, and psychic types? Too bad it doesn't learn any fighting moves until level 44, and bug moves until level 54. Have fun using Return for most of the game, and make sure to keep that friendship up!

Sneasel: by the time you can finally get this guy, his usefulness is already mostly gone. He'd only be good for the dragon gym... if he actually learned any ice moves. You have to TM ice moves, and you can't get Ice Beam until after the pokemon league.

Lanturn: on the bright side, at least by the time you can catch a Chinchou, you'll already have the HM for surf. So thats the water move covered. But electric? Gotta grind out 5 levels to get Spark. Then you're stuck with Spark as the only half-decent electric move until Kanto when you can finally move tutor Thunderbolt. Oh, and if you want to move tutor it, you've gotta wait for a Wednesday or Saturday and grind a bunch of game corner coins.

Xatu: So you want a flying/psychic spot on your team? Well you're stuck with Peck until you can get the HM Fly, and no Psychic until level 65 or Kanto where you can get the TM. But what about Dream Eater? Oh, right, no Hypnosis.

You probably want a Dark type on your team, right? Well theres a few options: Umbreon, Murkrow, Sneasel, Houndour, Tyranitar.

Hmmm. You can buy Larvitar from the game corner for... woah... 8888 coins. But it doesn't turn into a part Dark type until level 55, so you'll be waiting a while.
Houndour is exclusive to Kanto. Darn.
Can't get Sneasel until you've already beaten the ghost gym.
Murkrow is exclusive to Kanto.
That just leaves Umbreon... and friendship evolves in Gen 2 are the worst.