The career situation for physicians is difficult, and moving from insurance to a concierge practice is one way for their industry to survive and thrive. Many of the best medical students turn towards a specialty because the compensation is so much better, as a result of the way insurance companies reimburse doctors for services. Compensation is not just the simple issue of supply and demand, but that has something to do with it as well.
Society still needs primary care physicians even though they don't make as much money as specialists for the most part. To justify the ever-increasing cost of medical school, doctors need to seek higher compensation. A concierge model can increase the annual income of a practice. For the patient, however, the typical concierge medicine approach is incomplete. Insurance is still necessary - though perhaps an insurance plan that includes only catastrophic coverage - because once you need a specialist, without insurance, you'll need to pay for your care out of your pocket.