You're making a lot of assumptions: that providers are healthcare providers, that providers want to provide more healthcare, or that providers are incentivized to pay for better healthcare.

I'm sure the system you want would exist if healthcare providers had one customer to worry about: the US government. I can't think of a single doctor, the ones that actually want to help people and not cash a phat check, that likes the current system of filling out paperwork or begging to do surgeries for patients from insurance companies.

Most actually want to just provide care.

Get rid of the middle man, get rid of the profit motive, and you'll get a system that society can actually shape.