> Medicaid and Medicare are heavily subsidized in practice by private insurance covered patients. If we implemented single-payer in the form of Medicare as it is now, the healthcare industry would quickly collapse.
In addition to everything you said (which is true), Medicare's apparent success is also boosted by the portion of Medicare patients who receive their non-pharmaceutical Medicare benefits through a private insurer.
Original Medicare (which is the part of Medicare that is purely government-run[0]) has dramatically lower ratings for both medical outcomes and patient satisfaction scores[1] than Medicare Advantage, which is privately run. Medicare Advantage also consistently outperforms Original Medicare on cost as well.
Unfortunately, when statistics are cited for Medicare as a whole by laypeople and in mass-media, Original Medicare and Medicare Advantage are lumped together, giving the impression that Original Medicare is much more effective and well-liked than it actually is.
The same applies to Medicaid, but because that's state-run, the exact details vary from state-to-state. Overall, though, nearly ever state has some form of private management for Medicaid plans, and those consistently outperform the state-run counterparts, for reasons which are immediately clear to anybody who's experienced both firsthand.
[0] except for drug benefits under Part D
[1] In 2015, Original Medicare's patient satisfaction scores were lower than the very worst Medicare Advantage provider - they were literally the bottom of the rung.