@Much2learn, the reason why UIUC admits so much internationals is because state funding for UIUC has decreased dramatically.
As for bureaucratic rules, there aren’t good options if there is more demand for a major than there are seats.
You could do what UIUC does, and restrict at the beginning. You could do what many other publics do and restrict after entry (so that entry to a major is competitive). You could not restrict at all, but that likely would lead to many years of college beyond 4 as kids don’t get in to required classes.
Or you could keep the number of students far below capacity, so that students can switch majors easily, but that requires a lot more money to maintain excess capacity.