How, exactly, do they resemble the cooldowns? The MMO cooldowns that are ticking down mere seconds until they are ready to go again? Please be detailed.
And of course, the 4e encounter/daily cycle is still the same in 5e, they just renamed them to depend on short/long rest. Is 5e just an MMO? My god, DnD3 had at-wills, how far back does this go?
On this. One of the issues with discussing this particular topic is that people are emotionally invested in this.
For example, for people that truly love 4e, you will often hear the following two contradictory things:
A. 5e is terrible, because they discarded all the good things about 4e.
B. 5e just reused the 4e system, so if you like 5e, you really like 4e.
On the other hand, if someone didn't like 4e, they are often going to resort to language to describe a feeling it engendered in them; more often than not, because they lack the terminology to describe the feeling in very critical manner (and because they bounced off of it and will be talking to someone with a system mastery of 4e), this conversation will go nowhere.
This isn't uncommon. Think about keyboards that you might type on. You might have strong preferences for the keyboard- the key travel. The clickety clack that it provides. The spacing between individual keys. These preferences will be different between different people, but unless you are intimately familiar with these ideas, more often than not you will often resort to saying, "I just don't like that particular keyboard." But at least with keyboards these concepts have been studied and, for the most part, engineered.
A lot of creative fields don't have that same amount of thought behind them, and while there is a lot of critical analysis, there remains a maddeningly subjective component. One person's camp classic is another person's terrible film. Or, to bring it to the topic at hand, some people have a different level when it comes to suspension of disbelief. Why aren't the police responding to that shooting? Why do you hear the "pew pew pew" in space? Why is opening statement and closing argument in that three-week trial both less than three minutes? Etc. In other words, what works for some people, doesn't work for others.
Moving to the AEDU example, it's pretty simple. Let's concentrate on the "E". The issue a lot of D&D players had with the "E" (refresher- "E"ncounter) power system is that while it solved a problem that D&D has always had (the issue of "going nova" in combats) by making giving powers different cooldown periods (at will, per encounter, and daily) it make explicit and unavoidable that this was no longer interested in verisimilitude. For the first time, the game provided resources that would be regained not through the passage of time, but due to the needs of the fiction.
Now, there are many people that might say, "FINALLY!" But that isn't the same as a short rest. Which is, again, time-based. In addition, the different classes aren't balanced around a At Will/Short Rest/Long Rest/ system. For a lot of people, this is one of many example where the game, regardless of the good design, went too far and "felt wrong."
Is it that much weirder than, say, an ability that you can use "more times per day as you increase in level" (proficiency times per day)? I can't tell you. I can tell you that for a lot of people, it feels
different.
It's similar to the many issues with hit points. There are people that grudgingly agree with the abstract nature of hit points. But if you make it too "in their face," (damage on a miss, or the proverbial high level character who just jumps from their house down a chasm to go to work because they have the hit points for it), they revolt. Because everyone has a different tolerance level, and one person's "great design" is another person's "too far."