Georgia Tech also lets you keep your @gatech.edu address permanently, for free. Just having a .edu address does not prove you're associated with higher-ed.

When I signed up for GitHub, the free and a paid accounts were differentiated (to me at least) by the need to keep source code secure. If you remove that distinction by offering free student accounts, you'll end up with a lot of ex-students using them. The movie theaters out here in Arizona figured that out and now only offer student tickets on Thursday nights.

Any group of students trying to launch a website with any chance of turning into a profitable company will have figured out how to come up with $12/month.