I'm sure that's possible for a lot of kids and majors, but it isn't possible for them all. Classes aren't equally offered in spring and fall and the schedules sometimes don't allow a kid to do any major he wants. Also I'm guessing coaches pressure kids out of doing things like that or taking certain majors. In fact I know that happens to some kids.
Regardless, like I said I don't really know where I stand on the issue. I do believe pretty strongly that kids should be allowed to make money off of their own name though. Not necessarily making money by salary or any type of payment from the school, but I don't think they shouldn't be allowed to make a dime off themselves. I just find it ridiculous that the NCAA will market UNC championship apparel seconds after the horn blows with pictures of the kids celebrating, yet those kids can't do the same with their own image.