Voter ID generally isn't supposed to be proof of residence, its proof of identity; it exists to prove that the voter is the person registered, not that the registered person is authorized to vote.
Most IDs acceptable for voting do not prove authorization (or even “authorization but for the potential of disqualification by felony”), so not accepting college ID because it doesn't prove authorization to vote is...not well justified, even in the public logic of voter ID.
Of course, voter ID proponents have let out the private partisan internal logic lots of times when they thought only people aligned with their faction were listening, so we don't need to speculate why the rules are inconsistent with the public logic.
Voter ID generally isn't supposed to be proof of residence, its proof of identity; it exists to prove that the voter is the person registered, not that the registered person is authorized to vote.
Most IDs acceptable for voting do not prove authorization (or even “authorization but for the potential of disqualification by felony”), so not accepting college ID because it doesn't prove authorization to vote is...not well justified, even in the public logic of voter ID.
Of course, voter ID proponents have let out the private partisan internal logic lots of times when they thought only people aligned with their faction were listening, so we don't need to speculate why the rules are inconsistent with the public logic.