It doesn’t have to completely kill private. Many countries combine the two with standard medical, and optional private for better terms (eg. single room, chief doctor, better dental). Then there are the hybrid systems, like full public insurance through multiple insurers with private opt-outs under certain conditions (germany). Or full private but with single payee and standard coverage and legal guarantees of affordable insurance. Then public systems with some capped self-pay component to encourage self-discipline and not running to the doc with every sniffle. Honestly, almost any system is better than what the US has, which adds unnecessary cost and complexity at every stage.