It's a simple question with a simple answer.
Why do airlines require that pilots have degrees? Because right now they can. If the shortage hits them hard enough and they are no longer able to fill the flight deck we'll see what they do. Personally I know a lot of regional pilots in the States hoping that this happens, until it does I wouldn't bet on it because the major airlines still have candidates lining up down the street and around the corner.
As a question to the European pilots here, do cadets in Ab Initio programs need a prior degree or do the airlines track their progress throughout training to see if he or she will be a decent fit for them?