Does your state have particular expertise at running colleges? Maybe so, but some states surely do not. The National Center for Education Statistics estimates that states subsidize $19,200 per student.
A state can decide it is good public policy to subsidize higher education for its citizens. If so, the state faces a decision on how best to deliver. States commonly subsidize tuition for students at state-run colleges.
One perfectly valid option is to give the $19,200 to the student for use at any credentialed college anywhere, public or private. The National Bureau of Economic Research estimates that 29% of students would select a private school instead. Surely some percentage would opt for a public school in another state.
One historical objective of limiting the subsidy to in-state public schools is to keep the educated citizens in the state. Brain Drain. To meet this objective, the state could require a graduate move back to his original state for a certain period, or else the subsidy becomes a loan. A state might even get out of the college business altogether and distribute the savings to students for use as tuition elsewhere.
Clearly states are not likely to take this radical step, especially the ones that are better at football.