How is 4e different in this regard? Didn't normal skill checks work similarly than in 5e? There were skill challenges, but even with them it was the GM deciding the complexity and stuff, and of course what succeeding or failing in it actually meant it in the fiction.
I think 3e was a bit less like this, (and I truly mean only a bit) as it (IIRC) actually had more codified DCs and generally more advice on what exactly the skills can accomplish.
And of course the flip side of having codified "it does this" like the spells have, it that it does only that. With skills you can potentially be more flexible. And of course in some games magic works like this too, instead of having codified spells, you just have a freeform magic system where you might have "pyromancy" skill with which you can do different sort of fire stuff.