If son doesn’t want to go to free state school, I’ve have him start exploring other options which a cost cap in mind and let him find some other schools to examine. If he’s serious about the major it does limit options since many schools don’t have that and some might have tougher stat/score requirements than general student populations.
To broaden search, consider UG where you can follow up different major with grad work - friend’s D went of College of Charleston as art history major with historic preservation focus. Now at Notre Dame doing grad work in Architecture. My D was actually discouraged from looking at architecture because of low pay but it doesn’t matter if that’s your passion - but does mean you should avoid large debt since you will have trouble paying it back.
I wonder if he’s in the “I know too many average students who go there” frame of mind. That happens when you attend college near where you live. My D went to college in same town to state U. Met lots of new people (and actually lots of professor’s kids) and there were some high quality students. Try to get him to focus on availability of major and less on students.