Density isn't everything. A good 4800dpi printer probably prints at 300 or 600dpi most of the time, unless specifically tell it to do a high quality print. In any case, it's not often that one digs through their printouts with a magnifying glass to be able to tell the difference.
For a phone or tablet, I would trade pixel density above 300ppi for a higher framerate or better battery life. My Nexus 4 has choppy animations, and that is much more annoying than being able to see pixels.
I'm not arguing that resolution inherently makes absolutely no difference. Yes, 100 PPI is markedly different from 400 PPI.
As for your comment on printers, it's apples and oranges. For example, you can print a 150 PPI image at 600 DPI, and each pixel will be 16 dots.
Secondly, dots aren't a uniform unit, you can have many different type of dots for different printers.
Lastly, it really, really depends what you're printing. Newspapers go below 90 DPI and billboards even below 45 DPI. In short, any number is extremely dependent on context. Your numbers are kind of meaningless.
But as for my actual question, it's not whether resolution matters. Of course it does. Battery life matters, too, but having 1 century of battery life on your phone that you replace every few years, or 2 centuries, doesn't really matter, you'll agree. There's diminishing returns. And there's a cost factor.
So what I'm wondering: does the difference between 400 to 450 to 500 PPI create such an improvement to viewing experience, that it's worth the hit to battery life and the more expensive hardware you inevitably end up with when trying to push almost a million extra pixels. I'm not so sure, I'd much rather get a 720p display that's cheaper and lasts longer.
The main difference is graphics vs text. While bitmaps won't profit from a better resolution, text will. Sharper letters, no more blurring around the edges. It's a big difference in readability.
No, there NOT an appreciable difference in readability of Latin alphabet above 400 DPI, and 300 when a subpixel rendering technology is used. Unless they're doing careful side-by-side comparisons, test subjects need better than 20/20 vision to notice any major improvement over 300 DPI.
The truth is battery life and game performance take a huge hit, so the manufactures can put a bigger number on their spec sheet. The consumer is the loser of this idiotic DPI race.
Resolution does make a difference.