\usepackage{mathpazo} is pretty nice. Palatino plus good math fonts.

The problems with CM are twofold. First, it's an inconsistent and amateur remake of Modern, especially italics. The bowls and straight lines are different angles and widths. Second, the postscript converted version used on most platforms is weirdly, bizarrely thin compared to the original Modern, which does not make for a good reading experience.

As you point out, there are two variables here: Is it processed in LaTeX, or processed in something else, such as Word? And is the font Computer Modern, or something else, such as Times New Roman?

I think the renderer has much more to do with the readability of a paper than the font. The combination of LaTeX and Computer Modern is certainly pervasive, but if I had to pick one variable, I would rather read papers using a different font but rendered in LaTeX, rather than a paper using a different renderer to lay out a Computer Modern font. For an example of the latter, take a look at this paper, rendered in Word, with Computer Modern font and some LaTeX-based margins and spacings:

https://www.ticoneva.com/journal_files/DefaultLateX.pdf