Heres the real benefit I see to 3840x2160 (or 3840x2400). Whatever. I'll call it 4k like everybody else is.
The real benefit is that you can start treating your monitor like a CRT again, feeding it arbitrary resolutions. First off, 1080p would work fine on a 3840x2160, and with any luck the monitor would just display it pixel-doubled so it wouldn't be any more blurry than a native 1080p monitor. That would be awesome. You can also run 1280x720p natively, as 3840x2160 is triple that, just like its double 1080p. But heres the real kicker - say you have some old game that tops out at 1280x1024 or something. You'll have to accept the black bars on the sides for games that aren't widescreen, but given that, you can upscale 1280x1024 to 2700x2160 or whatever. It'll still look good because theres so many excess pixels - more than double. Back when we were switching from CRTs to 15 and 17" or maybe a 19 if you're lucky, we had the issue that 800x600 looked like junk on a 1024x768 monitor and 1024x768 looked like junk on 1280x1024. At 3840x2160, we can display 1080p and 720p with literally no artifacts, and anything in between with minimal artifacts. In fact, the dot pitch of a 3840x2160 24" monitor is smaller than that of a typical 21" fine dot pitch aperture grille CRT. 3840x2160 at that resolution is only .13mm dot pitch. Remember when we thought .25mm dot pitch was awesome? Obviously we've got that beat, and that's why 3840x2160 is worth it even when not displaying native 3840x2160 images.