Anyone looking for an awesome challenge for a nostalgic game should try this. I set out aiming to beat the game simply without catching any pokemon or BUYING any items, but I ended up completely avoiding the use of items (aside from the necessary HMs, and I did use two TMs... but the game is doable without any TMs). Anyone can beat the elite four with a single pokemon if they have enough items to fully heal themselves over and over. As well, I knew the game would be too easy if I overlevelled, so I didn't level anyone higher than level 59, with my team average being 50 all told.
Basically, the game starts with you making the choice between Bulbasaur and Charmander. Squirtle cannot learn cut and thus cannot advance far enough into the game to win. The only exception to this might be if you allow yourself to use a pokemon such as paras to cut the one necessary bush, never using that pokemon in battle, and then immediately release it into the wild.
Assuming you chose Bulba/Char, skill choices become critical because you only have 3 remaining slots since cut is permanent. Bulbasaur can make short work of the first 3 gyms, but Charmander is definitely a better bet in the long run, with mostly better TM choices for this challenge.
You get much more attached to your full team of 6 somewhat random pokemon as compared to having a plethora of choices, and there's far more strategy in TM/HM usage. In total, you wind up with your starter, your two fossils, whichever hitmon you got, eevee and lapras. These are obviously not caught, just given to you, so they're all you get.
I'm far from being an expert pokemon player, but for people who've played through a million times, this may be an interesting thing to try. I know I found it fun. :D
I don't use healing items when I play normally. Of course I catch pokemon, though.