> I know governments have numerous Supercomputers that blow past $200MM in build price, but what universities do?

Even when individual universities don't-- governments have supercomputing centers that universities are a primary user of and often charge back value of computing time to the university or it is a separate item that is competitively granted.

Here we're talking about Jupiter, which is a ~$300M supercomputer where research universities will be a primary user.

University of Illinois had Blue Waters ($200+MM, built in ~2012, decomissioned in the last couple years).

https://www.ncsa.illinois.edu/research/project-highlights/bl...

https://en.wikipedia.org/wiki/Blue_Waters

They have always had a lot of big compute around.