Single-payer healthcare is firmly supported by the left and centrists in America according to polling. But, it will never be instituted because the common approach to all government benefits for the people is entirely wrong and most often backward from our economic reality.
Despite numerous studies showing that Americans already pay enough via Medicare, Medicaid, VA, and various other programs to fund the entirety of our current healthcare system, politicians dodge the issue by insisting that additional taxation or premiums be levied to "pay for" a system that is cheaper and more effective than what we currently have. Doing so would be disastrous to our economy because single-payer is "deflationary", not a cost to the people.
I won't even get into the debate about whether taxes pay for the government and its programs at the federal level (hint; they don't). Instead, I would simply use the graph you presented showing the imbalance between Drs. and administrative staff. Most of those administrators would be forced into involuntary unemployment and need retraining and financial support until they could find suitable employment. We would owe them considerably more than what state unemployment programs pay and that would include retraining/education.
This number of potential unemployed people as a result of adopting a single-payer is estimated as high as one million by some fairly astute economists. Removing billions of dollars from the private sector isn't going to be an answer to such demand deficiency and would likely only make the need for financial support programs that much greater.
In its zeal to be seen as "fiscally responsible", Congress would most likely "tighten its belt" to squeeze out money to "pay for" something that doesn't need to be paid for, and that number would be large enough to throw us into a deep recession before we knew how wrong they got it. If we stacked such lunacy on top of the current mistaken concept of higher interest rates to cure inflation currently accepted by our Fed, (they promise it will work this time and not just increase inequality as it has historically) we might skip right over the recession and go to full-blown depression.