This is actually the idea behind Direct Primary Care[1]; basically the idea is that by not taking insurance the overall cost of care goes down due to the decreased overhead around the claims process.
My dad is a PCP who switched his practice over to that model several years ago. From what he's told me he prefers it a lot over the traditional model specifically because it allows him to have a subscription based model rather than charging per-visit. That means that his revenues are more consistent but also has the benefit of aligning the patients' and doctors' incentives more directly: the doctor makes more money when their patients are healthy than when they are sick so they're incentivized to do a better job.
It also meshes well with telemedicine and chat-based consultations. He was offering both of those options to his patients well before covid because it tends to save both doctor and patient a lot of time, and there's no concern over "how much do I bill for telemedicine vs a normal visit, and how do I bill insurance for it."
My dad is a PCP who switched his practice over to that model several years ago. From what he's told me he prefers it a lot over the traditional model specifically because it allows him to have a subscription based model rather than charging per-visit. That means that his revenues are more consistent but also has the benefit of aligning the patients' and doctors' incentives more directly: the doctor makes more money when their patients are healthy than when they are sick so they're incentivized to do a better job.
It also meshes well with telemedicine and chat-based consultations. He was offering both of those options to his patients well before covid because it tends to save both doctor and patient a lot of time, and there's no concern over "how much do I bill for telemedicine vs a normal visit, and how do I bill insurance for it."
[1] https://en.wikipedia.org/wiki/Direct_primary_care