I don’t think the system would change that much, save for insurance companies not having a say in the healthcare a patient receives. It’s ridiculous that insurance companies come before the health of the patient.
Here in Sweden, if you have the sniffles, you don’t see a doctor. There’s nothing a doctor can do for you. If you get really ill, you go to the ER. Assuming you’re not actively dying, someone who gets stabbed will absolutely go before you. The ER doesn’t operate on a first-come-first-serve basis. If you come to the ER with the sniffles you’ll get to wait for a long-ass time, and at most they’ll send you home with some antipyretics and a suggestion to book a time at a clinic if your problems persist.
There are obviously issues. Gods do we have issues. In general though, the quality of care here in Sweden is ranked higher than that of the U.S.