You're absolutely correct. Text sizes should be set in points rather than pixels.

I'm afraid I disagree with the ubiquitous use of serif fonts in body text. Generally, I find that serif fonts are harder to read on-screen than sans serif fonts, and there were a number of studies in the eighties (I think it was the '80s) that support that same conclusion. Serif for print, sans serif for electronic display (or for dot-matrix printers, but nobody really uses them any longer).

Serif fonts also make it difficult to display small fonts or to show text in very low-resolution displays without it becoming nearly impossible to read.