There's a large web of insurance companies, hardware and chemical companies, provider networks, and universities that benefit too greatly from the current inefficiencies to ever move away from private insurance. Hardware and chemical companies like LifeSys have contracts with insurance companies and provider networks that state the insurance will only pay for things if the tests or treatment are done with that supplier's tools and that the work will only be done if it's within the network.
For a theoretical based on what actually happened where I live, Hospital X is contractually obligated to use a specific kind of infusion pump from supplier Y and order blood tests from specific supplier Z in order to get Blue Cross Blue Shield coverage. Meanwhile the state university pushed out the other hospital in the city and heavily expanded the surviving hospital campus they sponsored to take on the increased capacity and introduce the services they were previously lacking compared to their now dead competitor. So Hospital X is just following the policy of University Network A. All of which is a common practice.
In many states the state university sponsored medical care networks are the or are close to being the biggest employers. The University Of Iowa medical network, the West Virginia University network, and University Of Pittsburgh Medical Center network all have taken over a majority of medical care functions in their states, leaving mostly specialists and those in mental health to independent practices. That exacerbates the issue of insurance and supplier contracts, because these small places that are competing with the university networks often don't bother with insurance unless it's government provided and just prefer patients pay up front instead. They lose too much time and money sorting through the myriad private insurance providers, plans, and coverage obligations without full time staff to handle that for them. Medical billing is a massive industry for a reason.
Now, if everyone wasn't chained to private insurance and juggling all of these providers, coverage limits, and contractual obligations the number of inefficiencies and thus the overall cost would decrease. We have historical examples of this even in the U.S., by comparing what happened between 1960 to 1975 and it's modern equivalent of 2005 to 2020. Healthcare costs were increasing rapidly, doctors were dwindling in number, and there weren't enough medical students for generalist fields in the 1960s just like the 2010s. The major difference is that while quality of care continued to increase through the 1960s and early 1970s, both the efficacy and quality of care has gone down since the 2000s. The several minor differences were that nationwide coverage was rarely available in the 1960s compared to the 2010s, that Medicare was spending more than it was receiving in the early 1970s thanks to how Medicare was funded in the 1960s, and that privatization of entire hospitals was uncommon and frowned upon in the 1960s because of the income impact it had on the doctors. The U.S. barely survived the 1960s medical crunch with enough government intervention, but it is dying under the weight of the 2010s medical crunch because the government can't easily intervene and is lobbied to maintain distance.
So the reason the lead figures in the American right are worried about single payer is because they won't make as much money. And they're very good at convincing people to vote against their own interests because they know those people don't care to look into complex systems too deeply. As a result many of the regular voters and workers are worried because someone told them a lie about where the money is actually being wasted and what the actual history is.