I find it interesting that this was considered a solution to the treadmill effect of attack bonuses and AC (among other things of similar nature). Basically it wasn't a solution so much as an exchange. You went from increasing attacks and AC to increasing damage and hit points (the "bloat" we all know and love...).
I have seen people post about wanting effects or reduced damage even on missed attacks.
Also, consider an abstract understanding of hit points, generally accepted in 5E (although some insist on still considering them all "meat"). I have long considered "hit points" more properly termed "combat effective points" given how they are "expended" to avoid serious / deadly injury. Really, they are plot armor to keep your character in the story.
So, I will do my best to express my idea about (at least) removing attack rolls from D&D:
Each concept is addressed in further detail later on.1. Damage increases with level. Starting point is +1 die per tier perhaps.
2. Damage dice explode to represent critical "damage" (replacing critical hits) for any die rolled.
3. Ability modifiers still apply to damage as normal.
4. Armor class (worn or natural) is translated into damage reduction. Start point is AC value - 10 = DR.
5. DEX modifier also reduces damage as a "dodge" or "parry". I don't know of heavier armors would limit this or not...
6. Size also reduces damage as a "cap" concept, 1 point per size difference.
7. Save for half spells might be reworked to a middle damage or perhaps keep saves?
More to come...
The idea is when someone attacks, the target expends hit points to avoid the attack. For the most part the attack is always effective in making the target defend itself (the loss of hit points given current terminology). How effective or damaging an attack is depends on a few factors: experience of the attacker, weapon being used, etc. as well as the defenses of the target.
For example, a commoner attacking with a dagger might do 1d4 damage. To an ogre with 59 hit points, the commoner with a dagger is not much of threat. The commoner's attack is easily avoided, soaked, parried, or whatever so the lost hit points is relatively small (avg. 2.5 out of 59 would be about 4% of the ogre's "combat effective points"). In other words, the commoner would need to make several attacks before the ogre was concerned. Or, a mob of commoners would be a threat due to their accumulated damage. (Note: the size difference DR is negated by the Ogre's low DEX. Any armor worn would provide more damage reduction.)
However, a 10th level rogue might do 2d4+4 (DEX mod) (+ 5d6 sneak attack maybe), averaging 9 (+17.5) damage on each attack. Now, the same ogre has to work harder to defend itself, expending more hit points to negate the attack. Just the normal dagger strike would expend nearly 15% of the ogre's hit points, while a sneak attack added in jumps that up to nearly 45%! The hit points expended by the Ogre to handle this damage might be, again, any combination of taking the hit (soak), actually injury, expending enormous energy skill to "avoid" the attack, or whatever fits the narrative.
So, part of bounded accuracy was supposed to be increased damage, but IME damage does not typically increase on the same scale hit points do. So, the above example would incorporate a system for increased damage. A simple suggestion would be adding one die of damage per tier or something.
It also means there are no "failed attacks". If you make an attack, you are actually attacking--your effort always results in some expenditure of hit points by the target. The damage roll (however that might be adjusted for this concept) determines how effective your attack is and how many hit points the target would expend to avoid / reduce / absorb / etc. that attack. Damage reduction and dodging (see below) can reduce damage to the point where an attack is rendered ineffective, however. Again, the idea isn't that you failed so much as the target's defenses might be better.
Without attack rolls, armor class would not exist as it currently is. Armor would provide damage reduction, allowing the wearer to more easily mitigate attacks. Armor (and size difference) would reduce damage to a minimum of 1, not 0. That is my first thought anyway...
Dexterity (not impacting AC) would also reduce "damage" but in the sense of a dodge or parry. Our dagger-wielding commoner attacking a DEX 14 target would deal 1-4 damage, but the DEX would reduce the result by 2, making half of the attacks "dodge" or parried or avoided by DEX alone. I think this form of DR should be able to reduce damage to 0.
Spells and other features that boost AC would likewise reduce the damage in some fashion, again decreasing the effectiveness of the attack.
Spells which allow saving throws (such as fireball) could be reworked slightly to average result (instead of 8d6, save for 4d6, make it base 6d6?) if we wanted to remove saving throws (in that sense) as well as attack rolls? Or saves could be retained?
The system could be built up without much difficulty, although many adjustments would need to be made of course.
So, I guess that's it for now. This isn't really something I am considering adopting seriously, just the results from some observations about the purpose of bounded accuracy, how likely attacks succeed in 5E, and other factors.
Also, I am not saying this is a good idea or a bad idea, just an idea. I welcome any discussion about it as an exercise in game design, etc. I am well aware people might not care for the idea of removing the attack roll, but frankly in 5E attacks seem to hit so much IME I wonder if there is really a point in having them anymore? 
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