I work with a lot of doctors that have moved into cash practices because insurance does not work in the area of medicine they practice in. It sounds like most of them took anywhere from 5-30% of their patients with them. The majority of patients are not eager to give up their insurance coverage for a doctor unless they find them irreplaceable.
I am currently working with one doctor that moved from a hospital to PP this year. He charges $350/hour and was able to immediately get about 10% of his patients to move with him. I'm guessing he had over a 1000 patients within his pool previously, so that's not a bad start. He's very unique in what he does so I think he'll continue to gain back patients as they realize they cannot replace him with a conventional insurance practice.
But, if you're just doing the same stuff as the doctor down the road does, good luck differentiating yourself and justifying the additional financial burden your patients will face.