Compare UPS or FedEx to USPS; the first two companies are profit-seeking, yet very competitive with the 'public-oriented' (and legally privileged) USPS. Having the government in control does not necessarily lead to better value.
They are very competitive in the places where most people live, but the USPS delivers to many more places that the others do not, and still maintains cost competitiveness.
This turns out to be a decent analogy to healthcare: insurance companies do not provide the coverage, universality and simplicity that a single payer system would; instead, you'll get something like insurance coverage networks providing spotty and inconsistent care.
Either approach has upsides and downsides, but single payer, universal coverage for basic and emergency healthcare seems like a no-brainer.
I've lived in cities where the city ran the utilities; they were generally way cheaper than the utilities from PG&E.
The USPS is obligated to deliver letters at the same cost to everyone in the country, and they do a pretty okay job at it -- I've certainly had horrid events from UPS and FedEx, and those guys get to just pass the crap delivery tasks off to USPS if they don't like it.
Lots of old people in the USofA seem to like their government run medical insurance, same with people in the VA system.
The Doge crew spent months looking for fraud waste and abuse and I don't see any big law enforcement results from all the fraud they found, and I don't see anyone crowing over all the waste they curtailed.
It's possible that the world's more complex than you imagine, and that sometimes people just do their jobs (IE the bureaucrats) and hard problems get solved.
Now, tell me again, what part of the health care system is UnitedHealth? What critical problem do they solve?