Anecdotally speaking, I run a 2K resolution monitor and had a game get within a hair of maxing the 11GB memory of an RTX 2080 Ti. Maybe on a 4K monitor it could have pushed up to that limit, though I'll admit that was only one game (that I can't remember what) and it could have just been a result of poor optimization, a fluke, or anything else I'm not considering.
I'd guess that maybe some more fringe examples exist, though I'll admit it's not really a good reason to suddenly start slamming a ton of VRAM on every new video card.