Because medicine isn't paid for as a government-provided service. Insurance companies exist to profit - they defer risk. It is not a public service. I have a pre-existing condition, and I have a very mild case of Cystic Fibrosis: my healthcare at market costs about $500k a year. There's a lot of nuance to how much insurance companies actually pay out, etc, but looking at it in a simplified manner, it takes 25 families at $20k in premiums a year (with no claims to pay out) for them to break even on one of me.
tl;dr Health insurance is a for profit product, not a public service.
Marketing, claims denial, billing and executive compensation budgets that together amount for 20% of the expenditure of an average US insurer after they were legally capped to that level.
Even eliminating those expenses doesn't really help much. It just changes the numbers in the headlines. $16k in premiums is still tough for most US families.
It’s still $0.6 trillion dollars saved per year, and a solid place to start. There’s all sorts of other places that a socialized system saves of course. This would at least make the US no longer far and away the worlds worst.
Bringing everyone under a single umbrella should reduce everyone’s cost of coverage to the per capita cost, $10K (now $8K after savings). Then as a progressive tax system yields costs that scale according to your income the least able to afford it pay much less than that and the most able pay much more. Done and done. This is what the rest of the world does, no new ground is being broken here.
tl;dr Health insurance is a for profit product, not a public service.