Not really it's easier if everything was the same doesn't have to be aedu.
All long or short rest or at will plus one of them.
5E class design all over the place eg rogue, warlock and cleric.
Well.... Not really. lol. It can be CALLED anything, and it can be dressed up in any clothes you want (although I will continue to insist that consistent nomenclature and universal mechanics are best). It still has to have the essential characteristics of A/E/D/U (the U part is less critical).
The reasons become pretty apparent as soon as you start thinking about it. There obviously must be 'at will' abilities. If nothing else every PC has some sort of flavor of a 'basic attack'. Nowadays even wizards and clerics have an At Will. While some of the details vary from 4e's 2 choices per PC (which itself had exceptions) it is logically got to be some small number of attacks and abilities which are always available. So the 'A' is realized (and already effectively exists in 5e, though some things like Battlemasters kind of skate the edge of it).
Likewise the 'encounter' abilities. They logically must be a resource, otherwise they would simply be an At Will, so we have currently in 5e not a huge consistency here, but every single class has something that is recharging on a short rest or per-encounter. Every fighter has action surge and second wind for example, not to mention BM superiority dice, which are really just an approximation of 'do this about 2x per encounter' and might as well actually be written as such (and could even stand to be 'use each of these powers once per encounter, up to a maximum of 2 total uses'). They could just as easily be, and effectively are, powers in the 4e sense. Again, logically, you need these sorts of things for pacing and resource reasons. Unless your game is simply going to present a 1e-like fighter, there's not much other choice.
And obviously there are plenty of 'daily' powers out there, although the non-caster classes often lack them (and again this is simply a problem). Of course even fighters do have daily RESOURCES in the shape of HD and hit points themselves, which are most useful to fighters. It would be nothing but good for the game if they also had one or two 'big bang' powers that gave them something more on a par with what full casters can do (and maybe these would include some 'U' stuff that is good outside combat, what a revolution that would be!).
If you're going to tweak things, you are ALWAYS going to come closer to this basic model. The beauty of the logic of the design of 4e was they simply went all in and did what had to be done, and called a spade a spade. It worked! We can argue about the details of the FORM of powers, maybe they should work somewhat differently than, and be presented in a slightly different way from, the 4e ones. But the core A/E/D/U idea is simply not going to die.