“We all say we should get the same care, but I got sick and tired of waiting for that to happen,” he added. “I decided to go for quality, not quantity.”

Besides more money, the calmer pace of high-end concierge medicine is also a major selling point for physicians — Dr. Matles said he never made it to an event at his children’s school until he joined MD Squared. But for Dr. Sarah Greene, it wasn’t really the money or the lifestyle that led her to Private Medical.

“I really have time to think about my patients when they’re not in front of me,” said Dr. Greene, a pediatrician who joined the company’s Los Angeles practice in October. “I may spend a morning researching and emailing specialists for one patient. Before, I had to see 10 patients in a morning, and could never spend that kind of time on one case.”

Getting in the door as a new hire isn’t easy. When it comes to credentials like college, medical school and residency, Dr. Shlain said, “at least two out of the three need to be Ivy League, or Ivy League-esque.”

In many ways, today’s elite concierge physician provides the same service as the family doctor did a half-century ago for millions of Americans, except that it is reserved for the tiny sliver of the population who can pay tens of thousands of dollars annually for it.

“I didn’t know this level of care was possible,” said Trevor Traina, a serial entrepreneur here who is a patient of Dr. Shlain’s. “I have a better relationship with my veterinarian than the doctors I went to in the past.”

What about everyone else? Mr. Traina doesn’t see much future for the conventional family doctor, except for patients who go the concierge route.