The text is sharper with a higher PPI even if the actual size of the text is the same. I have a 4k 24" screen, and text is much much sharper than on any FHD 24". Hell, it's noticeably sharper even than on my 14" FHD laptop. And sharper text helps with legibility, so I find I can actually use smaller font sizes more comfortably than the "regular" size on a lower-res screen.
You don't get more real estate, indeed, since that depends on zoom level. However, depending on your setup and habits, you may actually gain some. In my case, I use 4k at 100% zoom. I don't care for window decorations, interface icons and so on, so it's not an issue if they're small.
If you go up PPI by a percentage you can reduce font size by a similar amount. Too small to be legible? Literally move the screen closer. No need to magnify anything.
Have a 27" 4k monitor and a 42" 4k monitor? Move the 27" close enough that it takes up the same FOV as the 4k and you get the same experience.
This isn't like home theatre where you're constrained to the dimensions of a room (ie. wall or console location a TV sits on top of and seat viewing distance).
You don't want it too close, but it can be closer than that if you have normal eyesight. The line should be where your eyes have trouble focusing and add a small buffer. For me that's about a foot. So wherever you're comfortable looking at a smartphone (or really any object) is a good point of reference.
Otherwise this is a commonly propagated myth related to radiation from early TV sets.
You don't get more real estate, indeed, since that depends on zoom level. However, depending on your setup and habits, you may actually gain some. In my case, I use 4k at 100% zoom. I don't care for window decorations, interface icons and so on, so it's not an issue if they're small.