I didn't (and can't) downvote you, but in general you're simply wrong. You cannot add more costs to "remedy" a cost center. If an insurer takes on more clients, they might make more profit, they might mitigate some risks, but their costs will definitely go up proportionally with their client base.
I'd also like to propose a thought exercise for you. Imagine a private insurer. They have, say, 50K clients. They make a couple million dollars a year in profit and make many millions of dollars in medical payments. Next year they double in size, which reduces their risk of failure and improves profit margin slightly. The better profit margin allows them to reduce costs a bit to attract more new clients. The next year they do the same, and the year after. Then they start merging with other insurers while continuing to grow. All along, as their client base grows, they improve profitability (and/or reduce costs) and their business becomes less risky.
Suppose eventually all Americans use this one enormous insurance company. They have the power to negotiate the best rates with doctors, drug companies, hospitals, etc. They have such a large client base that there is no risk, just extremely predictable income and expense. They can get costs as low as the medical industry will allow because they have such a large base.
Now suppose that this one enormous company is simply a part of the federal government. What changes to make single payer not work when it was working just fine before the words "federal government" were introduced?