D&D 4E used static damage for monster attacks as the default, with a rolled range (of which the static amount was the average result) as optional. If I remember right, it was also supposed to be the default for player attacks as well, although none of the DMs I played with used it on the player side.
5E continues to support this idea. Although spells and monster attacks are given a die range to roll, the average result is presented first in the monster stat blocks.
I think it takes a lot of the fun out of the game.
Zak Smith is persona-non-grata in the OSR these days (and we won't rehash why here, that's not the point and any comments defending or dissing Zak will be deleted), but he did have a good post I remember defending the Classic D&D group initiative system. In that system, you roll for each side in the combat each round to see who goes first. His defense of it was that the rolls not only add variety/unpredictability to combats, they also work at building group cohesion and keep attention focused on the events unfolding at the table. And I think he was right.
Set initiative (3E through 5E style) makes things a bit easier for the DM to manage at the table. But as a DM and as a player, I've noticed that after a player takes a turn, they know they've got quite a while to wait before their next turn, especially if they're not in a position to be attacked by the opponents for that round (archers, spellcasters, hiding stealthy characters). And there are enough distractions in this modern world (smart phones, new web browser tabs, etc.) that we can turn to while we wait that it can leave players a bit out of the loop at times. Group initiative focuses the whole group during the initiative roll, and it tends to last longer no matter which side goes first.
Set damage for monster attacks isn't exactly the same, but I believe it was implemented for a similar purpose - to make things easier for the DM. But it has the unintended side effect of making combat less interesting. If the damage for attacks is set, I know exactly how many hits my character can take. If it's random, I am forced to make assessments of the situation, and gamble based on how likely I am to get hit, how much potential damage the monster might deal (maximum and minimum), and how lucky I feel. It makes each round of combat feel more visceral and engaging. As a DM, it sure gets players' attention if you announce a monster has hit a certain character and then grab one or more dice to see how much damage was inflicted. Simply announcing "You were hit for 6 damage" is not so compelling.
Dice rolls add variety and uncertainty. That unpredictability makes the game fun. That's why we use them. Many mechanics that are designed to reduce the number of die rolls may save some time, but I feel the loss of player engagement isn't worth the time that's saved.
(Yes, there was a recent in-game situation involving set damage dice in a game I played in, and no, the details aren't important.)
1 hour ago