To be honest sometimes Engineering degree qualified pro pilots know a bit to much for there own good.
Had a propagating crack in the skin on a wing. The flight was full of office Aero's/Mech Eng's with a couple of crusty Licensed engineers and some Admin types.
Tech'd the aircraft and when I told them the reason the flight was canceled, of course all the techie types had to go and have a look at it.
We had all sorts of cunning ideas about stop drilling it and some fancy speed tape work. Nearly had me convinced. Then a custy voice was heard to utter
"And who the
are you expecting to sign that off?"
A very good reminder I was payed to drive the thing not fix it.
An engineering background does give a slight advantage because you talk the lingo and have a better understanding of some of the system interactions. Personally I find interaction with the engineers is more fruitfull because I will have generally taken note of more "details" about tech issues than some of my collegues.
But it is a part in the big picture of flying the line. There are alot of extremely good pilots out there that don't have an engineering background and who also have a very good relationship with engineering.
Now if you wanted to debate if some sort of social work/physiatrist course would actually give you more benefit for working as an airline pilot than a engineering degree. It wouldn't take much persuasion to have me agreeing with you. But if the personality types that would be interested in such courses would be stable extroverts or what ever we are meant to be this week I wouldn't know.