On my general usage / gaming PC I have a 27"/1440P monitor.
I have quite a few games in my backlog that won't play nice in 4K. Mostly they're (pre-2010 or so) 3D games that don't have built-in HUD/GUI scaling (or mods that fix it).
I could play most of them in 4K, for native resolution sharpness - but the 2D HUD/GUI elements would then be too small to make them playable.
An example: Neverwinter Nights. It looks noticeably better in native resolution, but even at 27"/1440P, the GUI elements look pretty small (playable but not comfortable). On 27"/4K it would be just unplayable.
Luckily this one got a remaster, with a scalable UI... but it's still an exception among its peers.
For old 2D games, it doesn't matter - you can't play them in a modern native resolution anyway.
When we're talking about games, there are multiple levels of resolution. e.g. the original Neverwinter Nights can run in 4K, the remaster added UI scaling, but the textures still remain at their original (low) resolution.