The library of the university to which I went used to have one or two books out of X which wouldn't be available for check out, only for reading on site.

Sure, if a bunch of random people show up and take them all at the same time, which prevents actual students from using them, it may be a problem. In practice, I don't remember ever having this issue.

Access to the library was free for all, you didn't have to be a student or anything.