I would favor those with degrees but I don't think one who has achieved that will make a better monkey button pusher
Button pushing is a small part of this job. I like to say that we have a job that is easy to do poorly. It is easy to not study the weather before departure (or have any knowledge on how weather systems work) and trust the dispatcher. You can sit back and read the paper and never check your fuel, winds, engine gages, or follow your flight plan as your flight progresses. There are lots of things that can be done on a flight that probably will not make any difference that time, and nobody will know if you did them or not. Maybe that is why a degree is good to have. It shows that I can do well in that art history class I took even though I had no interest in doing it. Aviation can be terribly unforgiving.