That is somewhat available in at least some areas of the US. My family pays a very low amount to a singular doctor's office for a "membership" that basically covers the cost of everything done in that office, and gives us priority access to visits (under 48 hours), and will then refer us to any specialist doctor for care above what they have which is then covered under our work insurances.

And we get to keep the same family doctor since we don't get passed around by "who's got the contract this year" so the guy knows us and will push through things for us.

I do think a lot of people have just accepted "its bad so it is what it is" and never truly explored the options available in a lot of America, because its often not as bad as it seems.