I definitely share what seems to be the general sentiment of preferring more moves, but being ok with the limit, but I've had too ideas:
1) What would people think of a limited movepool that's a little bigger than four (6, 8 or 10 perhaps), that leaves a little more room but still wouldn't let anyone have an answer to everything.  
2) If hitting supereffectively too easily is your real issue, limiting the number of damaging types we can have.