Even if they are good at problem solving, a series of 10-minute appointments spaced out in 2-3 month intervals while they deal with a case load of hundreds of other patients will not let them do it. That's the environment that most GPs work under in the modern U.S. health care system.
Pay for concierge medicine and a private physician and you get great health care. That's not what ordinary health insurance pays for.
That's the crux of it. My only point was it's nothing intrinsic to training or ability; they're often hamstrung by the larger system.