^^^ I don't think we're immune from those sorts of things at all, but I think our exposure to those kinds of risks are lower. I really do think that the situation you discussed was a one time meddling by the government that happened decades ago. In contrast some of these medical fields have swung up and down and back up again in the space of 15 years (and we're talking about pretty huge swings).
I do agree that if the government can cause us some pretty serious problems to any profession. However, I do think that over the period of 20-30 years even the government has made quite a bit of progress in allowing the market to solve its own problems. In those years we have seen deregulation of many industries like Airlines, Telecommunications, and most recently, Electricity. I may be wrong, but modern government seems a lot less likely to get involved even in the area of healthcare (although I have no problem admitting that healthcare is the most likely candidate for direct government intervention excluding those industries with military significance).
In any case you bring up a significant risk that I hadn't thought of before. With the statistics showing that around 30% of current dentists are within 10 years of retirement age, the government may feel a need to get involved. However, I hope that our modern government leaves it up to the ADA to decide how to deal with a potential shortage problem.
