4K displays are overated. Such insanely high resolution is not very universal, so for example 1920x1080 BD movies, or even older games (games with low quality assets and textures) will look much worse when displayed at 4K. What's more, even if you want to play 4K content on your 4K TV/monitor, you will still need to take into account the size of the display and the viewing distance, because if your eyes cant see more than lets say 1920x1080 pixels from the place where are you sitting, so why even bother with 4K display.
https://stari.co/tv-monitor-viewing-distance-calculator
According to this calculator people with perfect eyesight need to sit at a distance of 1 metre from a 55-inch 4K screen in order to really see what 4K has to offer (I'm talking about visual acuity distance). I have never seen anyone sit so close, and most people watch this kind of TV from about 2-3 metres, from which even someone with perfect eyesight cannot see more pixels than good old 1920x1080.
Although 4K displays are overated, I still try to run my games at 4K resolution if only my GPU has enough resources, because aliasing and shimmering arnt pretty, and only downscaling can make the game wi5h crappy TAA look sharp and aliasing/shimmering free at the same time. Even 1920x1080p display will show way more fine details if game will run at 4K downscaled to 1080p, than standard 1080p with TAA running on the same tv. IMO that's why people think 4K makes a difference. It's not because their display has 8M pixels, but it's because picture itself is way more detailed.
I have a total of 4 displays in my house:
-55inch 4K LCD TV for modern games with HDR
-42inch Plasma 1024x768 for PS3-PS2/xboxclassic/GC games
-32inch LCD 1920x1080 for PS4 games
-27inch LCD 2560x1440p with HDR for my PC
WIthout upscaling even my 1024x768 plasma has very sharp picture from a normal viewing distance and on this tv downscaled 1080p is already enough, to make even blurry TAA game look sharp. On my 32'inch 1920x1080 tv I need to dowscale from 4K to make TAA game look sharp. On my 1440p monitor I need 6K, and on my 4K TV i dont even bother with downscaling, because 8K is too demanding and 4K with TAA looks acceptable even without downscaling anyway and especially with good sharpening.