It depends on the screen and the software. On Linux in Firefox this page's legibility is pretty poor. However, when I was reading this page on iPhone, it was perfectly legible.
Also, Computer Modern on the same screen, but rendered by Okular or Evince, when viewing a LaTeX document, is also perfectly legible.
When it is rendered properly, I find it very pretty and legible.
I do a fair amount of statistics research. I'm not sure I've quite found my holy grail of math typeface (although I can think of a couple that come close in different ways), but computer modern / etc was never it for me.
I can totally see how it would feel sort of comforting though. I hadn't thought about it before but it does remind me of old Springer texts, and I could see how that would feel "homey" or something. This conversation has me kind of "resetting" my perspective on it a bit.
I loathe the old school Latex look. I appreciate Latex as a markup language, but the computer modern fonts always drove me nuts.
To each their own though. It's interesting to me that someone else had the opposite reaction.