hdtv began as a way to replicate the movie theater experience at home.
Pick the best seat in the house, and the screen occupies 36 degrees of your visual field. It dominates your field of view, and it's immersive. Trouble is if you sit that close to a standard definition screen, your eyes see pixels--blurred details that should be there, but aren't.
So, more resolution, and a wider screen was needed. Sure, you can sit ever closer to a small hdtv, but it's somewhat uncomfortable ergonomically
Using the standard that the human eye can resolve one arcminute of resolution, 480p is good for about 12.7 degrees, 720p, about 21 degrees, and 1080p is good for about 32 degrees. 4k is good for about 64 degrees, which is just massive.
The problem is, a 40 inch screen, viewed at a distance of 15 feet is solidly in the realm of Standard Definition --it doesn't matter if it's 1080p or not; you'd need very good eyes to resolve any more detail than what's on a DVD. (Since I have a 39 inch TV, I can confirm that viewed from a distance of 15 feet, it's rather tiny. My couch is limited by a tiny living room, so it's rather closer than yours.)
As for "correctness", content viewed on a small, distant screen has a different impact than content viewed on a close, large screen. People with smaller screens tend to prefer sharp, grain free pictures. People with larger screens can tell that the sharpening algorithms have resulted in halo artifacts, and the grain scrubbing has reduced human skin to the consistency of wax.
But if you're not impressed by the idea that a TV can an should occupy more of your visual space; if you're disturbed by the idea that what's on TV should dominate your attention; if seeing films in a theatre of your very own seems inappropriate; then yeah-- 4k television is the ultimate boondoggle.