Hmm...that'd be interesting. It'd be similar to other turn-based JRPGs, because a lot of them don't require you to forget skills for new skills. But it'd require a completely different approach to the battle system in all probability...I mean, at the very least the PP system would need to be reworked, because otherwise you could triple the length of battles until you run out of moves. Can you imagine facing a stall team where Pokemon have access to more than 4 moves, and all of those moves have been boosted with PP Ups? You'd be there for days.
Moves would either need to be made weaker, or HP pools would need to be larger to prevent you from carving up everything in your path, you would probably need to do something about breeding for moves otherwise you could break the game even further...I mean, Mew would be TERRIFYING in this scenario too, because it can learn everything.
For all its flaws, limiting Pokemon to 4 moves has always placed a focus on strategic gameplay, and if you remove that limit you change the dynamic of that strategy. I wouldn't say it was better or worse, just different. But you couldn't just do that and expect the game to be any better for it...if anything it'd be worse if that was all you did, because it'd be too easy to make Pokemon that could counter practically everything with its movepool.
Being able to see and more reliably manipulate IVs would be better than removing them, I think.
