"In my game, the players roll all the dice."
It's a nice thought, and it certainly has its benefits.
-It makes the GM seem more like a storyteller and less like an opposing team.
-It speeds up the GM's turn, keeping players engaged.
-It removes the need for a GM screen, which makes the whole experience a bit more casual and comfortable (imho).
But I disagree with it on theoretical grounds.
You see, game mechanics shape the story you tell at the table. Even if you don't think they do, they do. Let's take 3.5 as an example:
When a fighter swings a sword, the fighter's player rolls the dice. But when the same fighter is trying to avoid a sword-swinging orc, he doesn't roll anything. He uses his static Armor Class number and hopes the orc rolls low. Why? Isn't the fighter still trying to win? Isn't the player served equally by attacking and defending? Why not give the player agency (or rather, illusory agency in the form of a random die roll) over protecting their character as well?
Here's why: if your game allows players to impale themselves with their own roll, then your game probably isn't gonna be that fun.
Truth be told, there is a chance this happens in my game. If a player fumbles an attack roll, there is a random fumble table result that allows the monster an auto-hit counter attack that could kill the player, I suppose. But that result requires very low HP, and then a fumble, and then rolling one particular result on the fumble table, and then rolling enough damage on 1d6 to kill the player. Rare enough to warrant the shock value? I think so.
Anything more common than that and I think you have a problem. I can see low HP moments feeling like those god awful video game quick-time events which force you to press a certain button within one second or die. "Uh oh, the third orc is attacking you! Better roll AC again, or DIE."
As a player, I can accept when a monster rolls well and KOs me. But if it was my roll that took me out of the fight, I'd feel stupid.
Another example from 3.5: saves vs. magic.
3.5 had a near universal mechanic of "offensive actor rolls 1d20 + modifiers." Why would the game suddenly reverse this rule for saves against magic? Was it a mistake? 4e seemed to suggest so....
I don't think it was. Where magic is concerned, expending a limited resource (spell slots) if price enough for casting a spell. Simultaneously asking the player to risk a total miss, which would then waste the resource completely, is just cruel.
Now, asking the defending monsters to roll instead doesn't guarantee a hit, in fact it hardly changes the probabilities at all. But it does transfer the illusory agency of a miss from the player to the monster.
Wizard rolls low when casting a spell: "Wow Magic-Bob, you suck. Learn how to be better."
Goblin rolls high when saving vs. a spell: "Wow Magic-Bob, that goblin sure is tricky."
See what happens? It was the same exact mechanical outcome, but a different narrative structure, because when the magic-user's spells all go off with roughly the same DC to avoid, no one can say the caster has suddenly become crappy at his one job, instead, the monsters just feel more capable.
And having monsters that feel more capable is ALWAYS better than having players that feel less capable.