I am in college and brew. It is difficult using an electric stove and living in a small apartment makes everything difficult. That being said, I did my first all grain and it turned out great.
But an all student brew club would probably create a lot of problems (underage drinkers, people looking to make moonshine/swill/turbo-yeast).
Ironically my EdWorts Haus Ale all grain is cheaper than Keystone, Natty, Etc