Option 3: Make the schools co-obligors on the debt. In a default, the school pays. I suggested that to a congressman once; he nearly spit out his drink.
Also there might be scale correlated to market demand. So if doctors are in high demand the gov backs it more, if it’s something with little market demand, back it less.
The school can really only improve the education they provide or make their admissions more stringent. If they are going to do the latter, we might as well go back to direct government support, no need to have a loans process and all that noise.