A lot of people (too many to quote) are commenting that the best way to get better at the blues is to get out and play it. That's definitely true, and good advice. But it's also true of almost every field I can think of, and it doesn't mean that school wouldn't help. Doctors learn a ton by actually practicing medicine, but that doesn't mean they shouldn't go to med school.
Studying the blues in an academic setting could be very valuable. From a music theory perspective, there wouldn't be a ton to do. But you could study individual styles of different players, transcribing their lines to see what makes them unique. You could also learn the history of the blues, the conditions under which it developed, its place in society, the stylistic developments, the important contributors, the commercialization of it, etc. There would, of course, have to be a heavy component of playing music with good blues players. But there's more to studying music than just learning how to play your instrument.
I also disagree with the argument that, because the blues is an oral tradition, or simple, or "something you just have to feel," that you aren't able to study it in an academic setting. You can study any kind of culture or art, regardless of how primitive or sophisticated it is. People study cave paintings. People study folk art. People study rock music. Why would it be unreasonable to study the blues?
Getting a degree in the blues wouldn't automatically make you a great blues musician. But if it's something you're interested in, there's absolutely no reason to shy away from studying it.
What you are describing would be a music history major rather than a performance degree. There have definitely been people who have made an academic career studying the history of the blues. I don't think that's what the OP had in mind, but I could be wrong.