No.
Rolling and doing simple math does not slow down the game enough. Without some randomness, the game is much too easy to completely predict and control the outcome of a battle.
If there was a campaign where weapons dealt fixed damage, e.g a dagger did 3+STR/DEX points of damage, a greatsword did 7+STR, etc. Would you be happy? Would it take away from the fun of rolling damage for you? Or would you be content if it sped up play?
For mooks and partly with attacks spells that use too much dice. I.E. if sneak attack critical is 14d6+7 I would roll 4d6+35+7.
simply, roll 4 or 5 dice max, and average the rest of even number of dice.