Because in the absence of a single-payer system, the private portion of this system risk arbitrates all the higher-risk patients to the state-supported insurance and/or medical care, thus bankrupting the government and/or non-profit systems. We see this happen again and again.
What countries with well-functioning healthcare systems don't have a base-layer single risk pool under a government system? Of course, almost all of these systems allow supplemental and/or optional private care, but they are still single-payer insurance systems.
Isn't that the whole point of the state from a market economy standpoint? To take care of the things that are unprofitable with compulsion/taxation? You can't bankrupt the government. It's got the power to print money. It can keep going as long as it can do so. It also has the power of legislation. It can regulate prices if it so chooses.
What countries with well-functioning healthcare systems don't have a base-layer single risk pool under a government system? Of course, almost all of these systems allow supplemental and/or optional private care, but they are still single-payer insurance systems.