I think you've identified the symptom but misidentified the cause.
The majority in the US (as of 2022, according to Gallup) believe healthcare should be universally provided.
The majority also believe it should not be a government responsibility.
Broadly speaking, the US position is "Our current system sucks and we should be providing people healthcare detached from presence or absence of individual insurance... But also the government cannot be trusted to successfully execute on complex national projects."
What is so hard about it?