M0nica, No matter what the status of the president he will generate enough material to form a library, with his name on it. the university that gets the papers will be able to attract scholars to use it and keep their name in the news.
No, when I read about Presidential Libraries, was quite clear that the data stored is government property and in USA government archives. There are only 15 sites, it seems. Only 6 or maybe 7 libraries appear to be in any way connected to Universities - not a burden to universities in the whole.
My point, however, was that no matter how inconsequential, unpopular, untrained, disgraced, mentally incompetent (Nixon, Clinton, Trump, Reagan, Eisenhower) - they seem to have libraries.