It is the road to Socialism. A free market means that some people will shop, compare and could reject health insurance. With government paying for private healthcare, what is the incentive for private healthcare to charge less or not charge more? After all it's not like the end user, the consumer will care because it is government that is footing the bill.
In order to control costs due to that lack of how a real free market would control costs (ie: consumers shopping elsewhere when they deem rates are too high), the government really has no choice but to take over or I suppose they could set price rates.
If they choose to set price rates, well we all see what happens there with power companies in Cali having their prices set by the Dem congress. They have not as much incentive to produce more or to keep supply up and service suffers worse. Which inevitably the same lefties than just decry the usual profit, "free" market and just have government take over anyway.
Again, it's not a question of if, it's a question of how many, as in how many steps will it take.