I am not sure if single payer would work. But I do think it would work better than the current system.
One thing government does well? National defense.
How much would it cost? Half-a-trillion less than the current system:
"Through the mechanisms detailed above, we predict that a single-payer healthcare system would require $3.034 trillion annually (Figure 3, Appendix), $458 billion less than current national healthcare expenditure.40 Even after accounting for the increased costs of coverage expansion, our data-driven base case includes $210 billion savings on hospital care, $111 billion on physician and clinical services, $224 billion on overhead, and $180 billion on prescription drugs (Figure 3). Consequently, per-capita annual expenditure would drop from $10,7396 to $9,330, equivalent to a 13.1% reduction"
https://pmc.ncbi.nlm.nih.gov/articles/PMC8572548/#:~:text=Through the mechanisms detailed above,than current national healthcare expenditure.