(I am not a fan of GURPS, though I was super into it for a few years. Love all the books, though.)
D&D had skills embedded in the classes and equipment and there were a few nods to skills, such as AD&D's Secondary Skills. In BX, a fighter was able to use all weapons and armor. Those are some mad skills! A thief, of course, had an explicit list of skills (which which they suuuuuucccckkkeeeeeed.) A magic-user had the skill of casting spells and being able to create new spells and magic items. Etc.
Equipment also granted a skill-like ability to PCs. If you had a 10' pole you had the skill of being able to prod at a trap from a safe distance. A PC with a lantern had the skill of lighting a dark room - a huge benefit.
AD&D, and also BECMI's D&D line, had lots of weapon skills.
The thing that I believe grogs have a problem with is when a player says "I roll Perception. What do I see?" Instead of saying "I look around the base of the statue. Has it been moved recently?" and so forth. The former represents reduction of the fiction to a straight mechanic while the latter represents clever puzzle-solving and more immersion in the fiction.
Of course both can exist together. After examining the statue, the DM might ask me to make that Perception roll. Maybe they already know that I'm gonna see the scrape marks but maybe there's something else to be seen - such as a trap switch - and the dice roll will indicate just how closely my PC looked.
BX D&D gives the advice of using ability saves (we call 'em checks nowadays) for those moments where there isn't an established mechanic. This is a default skill system wherein the ability scores coupled with the class determine what types of skills you are good at. The party magic-user, with their high Intelligence, should to a better job of recognizing weird items and knowing esoteric lore. The cleric's Wisdom should let them know more about obscure cults and shrines. And so forth.
One way that the use of ability checks (and default skills in modern D&D) can frustrate players is when a character who isn't the party's authority on a topic is somehow just better at dealing with that topic. For example, maybe the thief has a particularly good Intelligence and the wizard is only average. If the DM allows the thief to make Int checks for every weird thing they encounter, the player of the magic-user might feel slightly useless. "Oh, Niff the Nimble rolled well under their Int so they know a good deal about this weird order of Purple Wizards. But Jan the Sorcerer failed that Int check and knows nothing. Again."
The solution to that problem is don't let Niff the Nimble make Int checks for things in which they have no expertise. And when you do allow it, follow Moldvay's advice and give them a -4 penalty. Let that middling wizard have a moment to shine and maybe even forgo the Int check now and then. "As it happens, Jan has heard of the Secret Society of Super Wizards."
A bit of ramble here as I basically think out loud about skills. More to say, but I'll do it later.