Although SWA doesn't say they require a degree, if you looked at their new hire classes, there very rarely is a pilot in it without it.

Having a college degree shows dedication, intelligence and maturity. These qualities, and many more, are not frowned upon by the people in the hiring department.

I'm not saying that college is the only way to attain these qualities, nor am I saying all college grads have them, but it does make you look better on paper.