In time, the profs will retire, and undergraduates will become profs. Those will expect proofs to have been checked before submission.
Mathematics might fission into two fields, one with proofs that cannot practically be formally checked, ultimately akin to philosophy, and rigorous maths that will demand finite checks. Moving results from the former to the latter will occupy some. Exploring whether, and under what conditions, that is possible, for any given result, will have its own interest.