I think there's plenty of room for innovation but we should start from the principal that everyone gets full access to medical treatment regardless of their ability to pay.
We technically have this in the United States (for emergencies). It is illegal for someone to be denied emergency services regardless of ability to pay.[0] No government system guarantees "full access" to medical treatment there is some form of rationing everywhere.
Emergency rooms are required to stabilize a patient, not treat them or cure them. This is not universal care and it not giving everyone access to the medical system. One does not got the ER for things like cancer screenings.
From the link you provided:
Hospitals are then required to provide stabilizing treatment for patients with EMCs.
Access is a function of cost. If medical care is affordable for people near the poverty line then we will be able to solve the access problem entirely. (this is my goal) Governments, charities, and businesses will pick up the slack as they already do.
https://www.cms.gov/Regulations-and-Guidance/Legislation/EMT...