How about comparing AEDU to the classic source for controversy then? Vancian casting. Especially All Magic Being Vancian. The issue there is that it breaks immersion, feels non-magical, and breaks balance.
If you're looking for me to defend Vancian, I won't really do that because I don't like it.
However, the problematic element of Vancian is being able to do something reliably up to X times a day, and then not being able to do it at all afterwards. In that sense, a 4e rogue is somewhat Vancian.
The good thing is that all magic isn't Vancian. 3e presents sorcerers that don't memorize right off the bat. The vast majority of magic classes released in supplements were spontaneous or used even less Vancian alternate casting systems, most notably the warlock. Several alternate casting systems are out there, including OGL systems published by WotC in UA. So it's not hard to play a non-Vancian caster. More importantly, fighters and rogues don't have daily limitations, and those two classes themselves constitute a large proportion of all D&D characters. So while I'm not defending Vancian as being anything other than laborious, confusing, stylistically limiting, and unbalanced, it has a strong history and at least it's optional.
AEDU isn't.
But a spamtastic fighter is to me far more diassociated from the way a fighter thinks, moves, and behaves in skirmish combat than an AEDU fighter is.
I find this opinion rather bizarre. When you say "spamtastic", I assume you mean that some fighters repeatedly take the same action (attack, trip, etc.). But it doesn't mean the character is doing the same thing each time. A successful attack roll could represent any number of martial techniques. Combining all those techniques into one attack roll is very abstract, but it's very D&D. If you wanted to model martial techniques, I assume you'd use facing rules and a stunt system. I also assume you'd want an injury system, because hit points are equally abstract and it's hard to model the way a fighter behaves without describing physical status in more detail.
These things have very little to do with simply packaging existing effects in the AEDU system.