I'm the opposite of the OP. I like the way 13th Age handles skills. It's loose and freewheeling, not granular or simulationist.
It's also pretty broken. All too easy for one Background (13A skill) to cover a lot more than another, for instance. (Ironically, while I consider that a problem in 13A, in 5e it wouldn't be so bad, every check calls for a DM ruling anyway, so why not?)
I want to go back to something more like AD&D's secondary skill rule. Essentially the player would select a profession, and then when they go to do something, if they can relate the task to their profession in some way they get to add their proficiency bonus.
Seems simple & easy. I suppose it'd replace backgrounds, or at least the skill gained from them...
The vagueness of 1E "skills" caused problems for my group. The 2E NWP sucked more than any other iteration. 3E/3.5 skills were a nod in the right direction, but were (generally) only of value if you maxed out your favored skills, which is pretty binary. I don't recalled 4E skills, honestly. The 5E skills are a lot like 3E skills, in practice (binary), but address some math problems.
Ironically, 4e & 5e skills are very similar. 5e adds a proficiency bonus of 2 if you were trained, then boosts that bonus as high as 6 of you level or 12 if you have expertise. 4e boosted all your checks by 1/2 level, and you gained a +5 bonus if you were trained. The difference is treadmill vs bounded accuracy. Where both deviate from 3e is that, if you're trained in some skills, your bonus from training & leveling is the same in all of them, only stats and any other special modifiers change that, while in 3.5, that first rank made you 'trained,' but you had to keep investing ranks to keep up as you leveled.
As far as I can see, the primary point of Skills being a subset of Ability checks is to make it absolutely clear that every character can attempt everything.
Could be. But, the DM can always decide an 'untrained' character (or any given character for whatever reason) auto-fails or a 'trained' (or whatever) one auto-succeeds, before it comes down to that check. So, if one did like the 'trained only' aspect of 3e, as a DM, you can still effectively use it.