National level policing would have to expand to take over a lot of the roles currently handled by state police, and we'd see a lot more interstate commerce.
Public colleges would probably, for the most part, switch to private (not as large an income source or value in subsidizing the students). Actually, a lot of state programs would have issues, except possibly in heavily urban counties.
One amusing thing that would occur: Appling GA would probably lose its status as Columbia county seat/"state" capitol, though it might be interesting having a state capitol that hosts literally no government functions (no idea if other rural counties might be similar, but my Grandparents lived there, so I am familiar with that location)