If you do that, college loans will be given only to the risk-free people. It's good for the country that some people go to college and fail to become wealthy off of it. That's why the government got involved. It's wasting human potential, and keeps poor people poor.
So it's not simple. Realistic solutions that promote the country as a whole involve balancing different goals. One of them is avoiding the way colleges use the loans to increase prices without increasing education.
On the other hand, non-government backed loans will cause the tuition costs to drop precipitously...which then would cause the risk-assessment to be easier.
I don't think it's good that poor people get stuck with insurmountable debt, especially when a lot of college degrees don't result in well paying jobs.