TL;DR:
giving damage after a near miss is bad idea.
OK at first level, who cares, but later on at high levels,
feats or bennies will stack and extras and magic items will kick in
and soon it won't matter if you rolled dice or not:
"I stood next to the spellcaster, looking at him, and then he died, m'lord"
And we all know more and more damage bonuses will be added to the game over time, since to-hit bonuses will be scarce, as a way to keep up player DPR, especially for those classes that don't rely on multiattacks.
Every one of those damage bonuses will need to be worked "just so", to avoid stacking with this. Otherwise, as you say, just walking over to the foe will have them be dead, with no agency of the dice.
It's one thing for a 20th level evoker wizard to have an at-will fireball that auto-kills any creature under 3 HP on a successful save. It's quite another for a 1st level fighter to do that, with no save at all.
As soon as their stuff beings to stack up, fighters will easily be mopping up foes and removing them from the board on command. That level of precise control of removing pieces from the board, every round is insane.
They didn't make 5e's Magic Missile a cantrip for a reason. And this is better. It's a no-action cantrip on top of the fighter's usual attack routine, with no extra cost in terms of action economy. The end result of such an ability will be eventually boredom, at best, and vexation and frustration at worst.
Feedback showed that auto-success and auto-fail were not popular. Putting that into the attack routine of 3 core PHB classes is going against everything else the game stands for and has been vetted.
-People vetted Advantage / Disadvantage, they generally loved it : this mechanic bypasses it and makes gaining advantage, or having disadvantage imposed upon you by your circumstances, irrelevant. I.e. you could be prone, blind-folded and attacking invisible tiny flying creatures and you will kill them automatically with your huge, heavy, slow axe each and every time. Player fiat, overruling common sense and the rest of the combat rules
-People vetted Bounded Accuracy : this mechanic bypasses AC, so makes BA irrelevant.
-People vetted weapon damage die mattering in attack rolls via D6 expertise dice -> Deadly Strike -> Multiple attacks : this mechanic doesn't even consider magic weapons' bonuses, let alone mundane damage differences. If you're so great with using two-hands to attack with, why aren't you improved with magic weapons? Kind of removes the fun out of a fighting style catering to "Great Weapons", when it doesn't benefit from a greater weapon (greatsword / greataxe) vs lesser ones (longsword used two-handed)