The feds could make it happen by eliminating/heaving restricting Grad Plus loans but alas, “college” is good for everybody. 
A lot of lawyers like to think that that the grass is always greener, but the above is incorrect. The major restriction on med schools is the cap on the number of residencies that the feds will pay for (part of Medicare reimbursement, if I recall). Unlike law schools, which are generally cash cows, med school classes are really small and the school itself is really expensive to operate, and without the promise of federal funding…
Plus, think about the marginal operation of a LS: one additional transfer is $50k cash in the bank, with no additional increase in costs. 10 transfers == a cool, half million of profit.
In contrast, med schools have space constraints. They couldn’t add 10 additional students if they wanted to. No lab space for them, without major construction.