There is indeed a glut of JD's and MBA's, but even within that supply and demand plays a role. There is no glut of say Harvard JD's or Wharton MBA's. You can tell, for the price of taking the LSAT or GMAT, what you odds of getting a job after graduation will be. No such assurances in fields like media or advertising, where luck plays a huge role in getting a job and no just pedigree.
Medicine is probably one of the more stressful work environment to be in, often with work/life balance suffering, so while positions may pay well, it may not actually lead to a happy life.
Politics and luck play a part in practically every career field. Having parents who can help support and bankroll you into a high-end medical or law school is lucky in and of itself.
It's true there is no shortage of doctors wanting to live in Manhattan or San Francisco, but most of the country lives in smaller cities and rural areas. Even parts of Chicago have doctor shortages: http://www.uchospitals.edu/news/2013/20130227-doctor-shortag...
See: http://www.washingtonpolicy.org/publications/notes/looming-d...
This is true to an extent - the shortage is in primary care, but at the moment there are two issues with the field: the huge costs of medical training in the US and the fact that the cost of healthcare in the US is twice that of the rest of the OECD nations, tendency rising. Something will have to be done, but it's impossible to predict what is going to give.
Combined with the fact that medical training lasts ten years, it is an uncertain proposition.
Parents should probably shift from just saying their child is going to be a doctor or a lawyer, and focus on what kind of doctor or lawyer their child is going to be, as that could influence their salary and quality of life many times over.