This isn't a problem I am trying to solve, as I thought this should have made clear:
Bounded Accuracy replaced escalating attack modifiers and AC (the "arms race / treadmill effect") with escalating damage and hit points.
As so mine (sort of), but this discussion is about are they necessary?
Frankly, my players enjoy rolling damage more because now the excitement/ tension is will you do a lot of damage or a little? By moving the critical to the damage roll, this is still present to adding more excitement (rolling maximum) and because damage dice are smaller than the d20 happens more often. They also cringe more often when I roll maximum against them.
5E has roughly a 60-70% hit rate, often slightly higher due to buffs IME. It became so common that it started to
lose the excitement since PCs hit way more than they missed. I had one former AD&D player who was playing 5E with me and surprised to learn he hit with a roll of 6 at low levels (he was in tier 1, but I don't recall his level at that time). I told him, "Yeah, you hit a lot in 5E, it was designed that way."
So, the question I am postulating really is why bother having a roll if you are most likely going to succeed? It becomes unnecessary and slows down the game, adding little enjoyment.
Also, it adds disappointment when you
DO miss. Which is why some people like or want a system where you cause less damage (but still some) or some other effect can happen on a miss. This way you still feel like you are contributing.
The sort of changes (again, as a design experiment) would be more about an "attack effectiveness" roll. When you attack, you are nearly always effective in making your target respond (dodge, soak, injuring them, etc.). The "damage" roll, modifier by your offensive abilities and your target's defensive abilities, would then determine how "effective" your attack was. If the target has sufficient defenses to handle everything you dish out (i.e. damage), they can negate your effectiveness entirely.
Finally, I seriously doubt I would implement this for D&D, but after reading more about Bounded Accuracy I realized it became (IMO) the next logical step. There are systems out there that do this sort of thing, but more by making it a contested roll. I am further removing the hassle of the defensive roll by making it passive--as it is in D&D.
Hopefully that explains everything in a clearer light.