You can get your SSN if you work as a student. Thats how I got mine as well
While I dont deny that it is a pretty stupid rule, all that I am saying is that it is just ONE of the worst of the stupid rules you find all over (especially for us internationals).
Most states require that you have a SSN OR you can prove that you are not able to get a SSN, or in other words you need to get some letter from the immigration authority. But anyways... this is a stupid rule not a preventive rule because and the legals are not allowed to drive (an elementary human right)

and Mich is the only state with such law

, but they have realized their mistake since they are already trying to change it.
Also, you can have a SSN without an H1 visa

I have a SSN and the only type of visa I have ever had was F1, but I got my SSN because I worked on-campus at my undergrad.
dosa_don
I dont think Michigan is the only state with such strict rules when it comes to licenses. Nowadays most states require you to have a SSN before you get a license. You can get a SSN only when you get paid for working, requiring you to have a H1 visa (I think B-school students should be able to get it). So it is quite difficult to get a license but to the states defense, it is aimed to preventing some level of licenses to illegal immigrants.