That was an articulate post, thanks for taking the time to write it. I understand your mental disconnect with diegenetic and non-diegenetic (interesting word choice, by the way). But I think it's a valid thing to do in the course of making the game fun. I think if you want more realism, if you'll pardon the abuse of the word realism, in the game it makes more sense to switch to a more skill-based set of rules anyway - GURPS, Hero, White Wolf, JAGS, etc... Because levels are a similar kind of arbitrary framework that don't make sense inside the game but make things easier at a meta-game level.
The particular problem with using critical hits in Dungeons and Dragons instead of some sort of meta-currency is that the critical hit system that has existed in every edition before 5 isn't that potent. I haven't read about the critical hit rules for version 5, maybe it's improved. Critical hits in earlier editions are not useless by any stretch, but even if your DnD3 fighter uses a lance and has Weapon Specialization, and is against an opponent that is not immune to critical hits, he's got at best a 15% chance to do triple damage. (Maybe 10% or 20%, I don't remember.) It's better than nothing, but in a climactic battle scene it can't hold a candle to the effects of a cleverly targeted Charm Monster spell or Fireball or Improved Invisibility. Not even counting Dungeons and Dragons 3/3.5, even in earlier editions with spellcasters that were weaker than their 3e counterparts, at high levels they still handily outdid Fighters for combat utility.
So if you wanted to replace meta-currency with critical hits or something else equivalent, critical hits need to be improved. Or possibly a Fighter's base attacks and damage need to be improved, so he doesn't need better critical hits to be awesome.
I grant that in theory in Dungeons and Dragons and in practice in many other roleplaying games, all characters do not need to shine in combat. As long as every character has a fairly common chance to shine at something, the game should be fun. However, Dungeons and Dragons has had a very strong combat focus since the earliest editions. So even if we remove the magic-sounding encounter and daily powers from 4e from the newer editions, it's likely that 50+% of gaming sessions is a battle. The person playing the cleric that only heals well and especially the one playing the thief that only steals well are going to spend a lot of time twiddling their thumbs waiting for lucky dice rolls in order to feel useful, while the fighter and barbarian (and especially the wizard) are going to be highly effective.
And of course, it's worth mentioning that Earthdawn turns this problem on its ear by making every PC class explicitly magical. So the Fighter can have magic-sounding cool powers because he's actually using magic. I loved the game concept, though Earthdawn seemed a little too complicated to me. I never actually played, though, maybe it works better in practice than it appeared on paper. I keep hoping Earthdawn will get ported to another gaming ruleset, but no such luck.