Every argument (that I've seen) in favour of AEDU has a counter-argument.
Every piece of descriptive logic (that I've seen) to explain AEDU falls to pieces when examined properly.
For me (and I gather many others...) AEDU makes the RPG into more of an rpG.
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See my rationale on page 2. If you take Encounter and Daily powers to represent player agency to declare when the combination of skill and environment makes it possible to do the action, then I think it holds up pretty well. It does assume that the in-game reality that the character is experiencing is more than the player experiences but that seems to be a long established tradition in D&D. The player declares "i try to hit the orc with my axe" but the character might be testing defenses, doing footwork, etc. also during that round. A round/turn is an game abstraction that gives you a lot of leeway.
Now, your second point I can't argue against. Your position seems to be that you can tolerate the gamist elements that have historically been there (HP, combat rounds) but it's not D&D enough if previously simulationist abilities become more gamey. Given my rationale, Martial and Daily Encounter powers are very gamist. If you feel that going there is just not your preference for D&D then I hear you -- different strokes...
I'm not sure, however, how you can say that martial Encounter and Daily powers can't make sense under any lens. They can easily make sense if you aren't trying to map them directly to an in-world character centric ability (and these abstractions have a lot of precedent in D&D).