I don't think the major universities - the ones that could have publishing houses that matter - are too broke to be able to keep the publishing house running.
I think historically the larger presses were expected to be close to revenue neutral. They do well enough to limp along, but don't get the resources really needed to build new infra. As a cost center without significant tuition or grant funding, the library has little pull when provosts form their priorities.
Look at the size and growth of the university's endowment.
Also, isn't the case that it is mostly the "major" universities that have their own presses in the first place?