When most of us baby boomers were in college (40+ years ago) college students were expected to register and vote in their home district. A student's college address was not a permanent residence, and in most cases your college address didn't even show on your student ID.
When voters are required to show your ID, it needs to include your permanent residence which would be your parents' address if you're an underage student. So for that reason college towns didn't have a lot of out of state students registered to vote because the kids were voting at home.
Nowadays, more students use their college address as their permanent address for identification purposes. That carries over into drivers license and voter registration records, but not every college town has accepted or encouraged this. It sounds like some are even discouraging it, but of course that would be illegal.
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