[impendia]

I am an academic researcher (math). Unfortunately, prestige hits the mark.

Whenever I am being compared with my peers -- for raises, for possible grant funding, if I apply for a job at another university -- people will look at publication lists and see who has published in "good" journals.

And when you say that "prestigious journals are widely read" -- honestly, journals aren't really ever read as such. Researchers will look for individual papers they're interested in. The choice of journal is a signaling mechanism and little else.

It is true that universities want prestige... but, honestly, tenured faculty don't often care too much about what their employers want. What a panel at a granting agency thinks of my record, is more important than what my department chair and dean think.

Your idea that e.g. Stanford should order their faculty to publish on SciHub is an interesting one. For better or worse, university administrators don't tend to have or exercise much authority, and any attempt to order faculty to do anything is likely to be met with fierce resistance.