It takes the difficulty out of the game to have a ton of moves. Restricting it to four keeps it challenging and forces you to choose wisely. It wouldn't be fun if everything could cover all its weaknesses with a single move. It's also because the games only have so much programming space, so they can't carry a ton of moves and still process properly.
Also, if you make the change to it, then you wouldn't be able to transfer pokemon from previous generations over very well, and as the transition from G/S/C to R/S/E showed us, people like having their old pokemon.