Actually I don't have it backwards.
The human eye can't tell the difference in pixel density on a 1440p 27" display and a 4k 27" display when the monitor is placed on a desk and sitting over 12 to 16 or more inches away from the user (which is normal for a desk setup).
Also the text on a 4k display is also extremely small. So if you tried to "display more", by having multiple windows open and up on a 4k display you wouldn't be able to comfortably read any of the text without scaling it up greatly, which would then defeat the purpose of this kind of "advantage".
4k displays on huge TVs and projectors makes sense because it allows you to sit very close to 70, 80, 90, 100" screens without a massive loss in clarity. If you sit far enough away from a 50" 1080p screen you get the same clarity, but with 4k it allows for same / better clarity if you sit closer or have a much bigger screen.
Places 4k displays make sense:
VR headset Screens (the screen is so close to the eyes so high pixel density is warranted). GPU hardware capable of pushing that man pixels is another story, and 1440p VR screens are good enough for a great experience, but 4k can be justified.
Huge displays (sitting close to very large TVs, and huge projector setups).
Places 4k and up doesn't make sense:
27" computer monitors
Smartphone screens.
Good game.