Yes, we already have that in many major counties in Texas, and it seems to be working very well. We provide universal healthcare, unlike the rest of the country, and yet taxes are still low, and people have a choice of providers.
I would still make some recommendations that would make it better. Now we just need to refine and duplicate the model nationwide.
Yes, unfortunately it does not get a lot of publicity. Most people outside of Texas don't even know something like this exists.
Here is the one for Harris County, Texas. #^https://www.harrishealth.org/about-us/harris-health
Other major counties in Texas have this as well.