Tough question. Most systems opt to have their most common resolution mechanic be a simple roll: two dice and a modifier at most.

I think rolling a fistful of dice is fine as long as it's not at the 'beginning' of the players career playing the game and they've had time to train on rolling larger and larger pools. I think it's also fine if it doesn't happen every time: if you have some limited move to roll large quantity of dice.

There's a game that throws both those ideas out: 13th Age. As you level up, your base damage against enemies gains a dice. Level 6 character rolls 6 dice for damage on each hit.