Med school is hard to get into because way more people want to get in than there are spots. In other words, there's a shortage of spots. So, let's crank up the econ. You get rid of a shortage by increasing quantity supplied or decreasing quantity demanded (or both). Increasing quantity supplied would entail opening new medical schools and/or expanding existing ones. But there are barriers - institutional and economic (because of the huge initial investment involved in setting up a medical school). Also, marginal costs of training extra doctors by existing medical schools will go up steeply because current facilities are already being used near capacity. This means the supply curve at this point is pretty inelastic. So we're stuck with supply.
How about demand? Well, however much premeds hate to admit it, going into medicine is an economic decision - there will be a cost at which it is not "worth it." We obviously have a surplus of people willing to pay $200K for a medical education (I won't go into residency for simplicity's sake). So a bunch, but not all, of them would be willing to pay even more than that. Take the price up high enough and the quantity demanded will decrease enough so that we reach equilibrium. Is that fair to poor students? Heck no. Will some of the people who bail be the smartest, bestest future doctors (whose opprtunity costs are probably the highest)? Yep. But admissions will be easier! (Another option to decrease demand is to lower physician salaries, which wouldn't necessitate raising tuition so would be easier on poor students, but has the same problem of running off talented people. However, if you just want very committed, dedicated physicians, lowering salaries would be a fairer way than hiking tuition to achieve that.)
In a normal market situation, supply and demand would adjust on their own. Unfortunately the med school market is royally screwed up (in economic terms). Barriers to entry keep supply from expanding, and fairness considerations keep tuition from rising in response to market pressures.
My vote is to use subsidies to overcome the economic barriers to entry, those freakishly high startup costs. This is justified because of the externalities associated with having enough physicians - benefits that aren't felt by the people paying the costs of training them (ie the med schools). The high marginal costs at this point come from the enormous fixed costs of opening new schools. Once you get past that, marginal costs settle back down. So tuition can stay more or less where it is, and I think it would take more new schools than we're ever likely to see to deplete the talent pool to where unqualified people are getting in. I'm only advocating this to a point, because beyond that you will have talent issues with admissions and eventually salaries for doctors will go down, which will further discourage talented people from choosing medicine and make those of us already committed to medical careers unhappy. Considering the condition of most state budgets, I don't think there's much government money around to subsidize new med schools. Which makes my proposal pretty unlikely to ever happen, unless...Bill Gates, are you listening?
If you're still reading you have too much time on your hands. Clearly, so do I. And yes, I was an econ minor. Why do you ask?