I think it's because traditionally computer screens have pretty low DPI, and serifs can be really tricky to render well at low DPI. In print, that's not an issue, and serif fonts really shine.
On high-DPI screens, like the one I'm currently using, serif monospace fonts can also look really good. For example, I'm typing in Latin Modern Mono (based on TeX's default typewriter font) in this text box.
Luxi Mono is great. Do you have an opinion on Go Mono [1]? It's by the same creators as the Luxi fonts (Bigelow & Holmes) and very similar to Luxi Mono but fixes some legibility issues. Moreover, it's freely licensed.
On high-DPI screens, like the one I'm currently using, serif monospace fonts can also look really good. For example, I'm typing in Latin Modern Mono (based on TeX's default typewriter font) in this text box.