How long ago did 300dpi printing become obsolete? These days I usually print drafts at 600dpi, because laser printers and LANs are fast enough that it's not annoying, and I don't usually explicitly notice jaggies at 300dpi, but you can still tell that the higher resolution looks better, if you care.
But that's black and white text printed on dead trees, not screens. Sure, it's harder to notice minor resolution differences with color photographs than with letters that have well-defined edges, and even harder to tell with moving images, but if you're using anti-aliased text on your screen, because it just looks better than non-anti-aliased, that's because you need more pixels. And yes, you've got enough GPU horsepower these days to trade the processing needed for anti-aliasing against the higher screen resolution, but you're doing it because your screen resolution isn't high enough.
I'm using a 17" 1920x1080 screen, and I'd like more pixels. This is generally good enough, with anti-aliased fonts, and the 22" 1080p screen at my office looks surprisingly good, but I'd still prefer 2560 instead of 1920, and the big advantage of 4K would be to have two readable pages side-by-side, which means more pixels vertically. (Sure, 16:9's fine for watching movies, but that's very seldom what I'm using that screen real estate for.)