If someone were to snap their fingers tomorrow and make it so that scientists could publish their work without having to deal with these for-profit publishers, universities would save millions of dollars (per school), taxpayers would save money, and the general public would also have greater access to the work that they themselves funded through public grants.
[1] https://www.universityofcalifornia.edu/news/why-uc-split-pub...
There was also a big fight over prices with Nature about 10 years ago.
This statement makes me think you significantly misunderstand how scientists / universities function. The scientists (graduate students, postdocs, professors, staff) are all salaried employees of the university. The university does take some of the grant money given to lead professors (e.g. to pay the aforementioned salaries).