Right, it's damning with faint praise. So I don't think it's a worthwhile objective to try to make skills be as exciting as combat was in OD&D.
I'll be upfront here: "combat" and "as exciting as in OD&D" are two phrases that don't go together IME. Its one reason I bailed out of it early. I've noted before that, barring the GM doing largely ad-hoc rewarding, non-spellcasters had two meaningful choices in OD&D most of the time: what weapon you used, and your target, and barring use of some weapon-vs-armor chart, the former added up to "what does the most damage". I'm not sure I've ever seen an RPG that had
less interesting combat for fighting types.
And it really doesn't take much to make it feel like your choices matter in combat. Some basic movement and position, cover, a couple different choices other than "I swing my sword" and it can be pretty fun. (One of the many reasons I tired of The One Ring is that combat was just too repetitive.)
It doesn't, but OD&D did virtually none of those, at least as a default in the system. At best you could use a chokepoint sometimes. But only sometimes.
You keep saying it can be done ("it" being to design a general purpose skill system that is like a halfway decent combat system, where player choices matter). So...where is it? Who has done it?
I didn't say general purpose. I think it can be done for individual kinds of tasks, and I've seen that in multiple games (heck, I know of at least one game that had a process
for custom building such systems if you were willing to do the lifting to do it; I used it for a comple of frequent events in the one campaign I used it for). As I noted, some skill usage
isn't going to be engaging, because it is almost always all-or-nothing things that are pretty much one-off (I've mentioned jumping before here). But those aren't everything.
The question ends up being, are you willing to deal with the overhead having a more elaborate system for swimming or climbing or building fortifications will be in such a system? The reason you don't see it often is the answer is usually "no". But then people bemoan that non-combat things aren't as interesting.