You felt the need to repeat it three times? OK, I got it, it was called Evasion and not Uncanny Dodge. Fine.
It was twice. Unless you were counting the amount of times I said the word itself then it comes to four times.. twice per description. But yes it is an important distinction. I got told over and over how it wasn't healing surges that I had an issue with (though it was) it was the second wind mechanic (I dislike that too). Specificity is important in cases like this - especially when you are wrong in your terminology - as evasion did a thing and uncanny dodge did another.
So, you evaded a fireball with nothing to evade behind, and nobody else except the character with the Evasion special ability could do that. Even if they had a much higher dexterity bonus than the guy with the special Evasion ability. Even if you were stuck in a pit with nothing at all to provide any vague cover to evade with, and the wizard fires a fireball on your head from above.
Everyone was hit for half damage or full damage, except the guy with the special ability Evasion who could reduce it to zero because "Evasion".
There is a problem with evasion, absolutely. It could be changed to make it more realistic and to make sense. The problem however isn't with how it interacts with HP or the attack. And the solution to fix it - to make it make sense - involves giving the rogue a free move which opens up a whole other nest of problems. It is a mechanic that makes sense and is needed, as long as the guy with evasion is supposed to be able to not fall for traps and fireballs from wizards.
Why is that more believable to you than this mechanic, where everyone either hits or misses with a melee attack, but the one guy with the special ability can do half damage on a miss?
This however is the opposite thing.
Let me give you a similar analogy.
I have a problem with a car that goes 300mph and also are able to somehow fly because they are going soo fast, even though I think that doesn't make any sense (and is impossible). Further, I say I dislike you trying to make it that ALL cars should go 300mph and be designed to fly. Your reply is that submarines can submerge even though that doesn't make any sense as air is lighter than water and should keep the sub afloat.
I guess the answer to your question goes something like...
Specific fighter can use this ability to deal damage on a miss, which no one else can do.
All rogues can use evasion, which no other class can do. Except, other classes CAN do things that replicate evasion, and it isn't restricted to a single class - and the evasion ability MAKES SENSE. You use an ability to bypass the damage. It should require you to be hiding behind a wall or cover, but it doesn't. To require it to do this causes more problems.
The fighter can use his ability to deal damage on a miss. No one else can. Even if they did there is no good reason why ONLY the fighter/DOAM'r can, nor why they get to break the hit/miss economy. Allowing them to do this doesn't make sense, as everything they are described as doing is already PART of what they do in the existing attacks vs. AC structure and hit/miss. Also, removing has no problems, KEEPING it opens up a can of worms that do not make sense.
As I would define it in the fiction...a "hit" that doesn't kill me is one where I should, by all rights, be dead. That otherwise decapitating blow was stopped by my gorget, my helm stopped the curshed skull, or maybe I took a wound, a cut, or a bruise, or a minor broken bone, that could have been fatal.
Meanwhile the "damage on a miss" is more like, I've done everything right, I held my sword just so, I moved my shield to block off that avenue of attack, or I somersaulted at just the right moment to evade the blade, but the fury of my opponents attack still managed to take some wind out of me.
Rage. Damage Reduction. Poison. Power Attack. Full round attacks.
I've just named five existing structures that are all affected by what you just say here to try and justify this new mechanic. Rage or otherwise hitting them with "fury".. except people with rage (Barbarians) don't get this ability do they? Block the attack, yet still deals damage? Yeah that works against DR which requires some form of reducing the damage of the attack. Poison should also go through if you are still hitting them. Power attack should surely grant this, on a miss. Because of the fury thing. And if it is justified as "I tried to hit, it got deflected and then I used my elbow" or whatever... that is an iterative attack (first attack sword (misses), second attack unarmed strike (hits?-automatically??)).
On optic, I don't have a problem of damage on a miss, as I don't see all hit points as meat, nor a round of combat as a single attempt each round.
That's nice for you. I DO have a problem with that, I do see HP as meat, I do see combat as (usually more than) a single attempt each round. And?