You'd be foolish to think that what type of degree you get doesn't matter. If all other things were equal between two candidates, but one has a PE degree and the other has an engineering degree, which one do you think they will hire?

You can view the degree as a check in the box if you want, but most companies read a bit more into it. Many want to know how well you did, especially if they are going to invest money into training you. They want to know you have a history of performing well in a training. While physically flying the plane is a monkey skill that just about anyone can learn how to do, knowing all the other aspects of the industry that apply is more book learning. To that end, if you do get a degree in golf or painting, at least you have shown that you can pass a classroom environment and you are a better bet on successfully completing an expensive training program vs the guy who does not have a degree.