The real poison is public funds => private hospitals. That's the #1 ticket for cost explosions. Private companies have unlimited appetites for money, and politicians have almost unlimited ability to produce money. It's a bad combination especially when you consider campaign donations from the companies getting taxpayers money.
When you have a massive government spending like America's Medicare, and that money is going into a "private" system, it distorts free-market pricing. e.g. if you work out the optimal free-market price of a procedure, then raising that price will lower the number of people who take it. But when Medicare is factored in, you can raise the price without lowering the number of people who take the option. This pushes up the prices for everyone, whether or not they are eligible for Medicare. So they raise prices to the optimum point to gouge medicare for every cent, this drives away a few customers who can't get medicare, but not enough to offset the big profit increase.
Whereas you can have two parallel systems operating much more efficiently. Have a private hospital system which is entirely paid for by the public through private insurance, and a non-profit public system which is funded directly by the state. The state naturally wants to keep costs down, but still get elected, so they will fund a reasonable amount to the public hospitals, neither high nor low, and it's the people paying the bills who appoint the hospital's executive staff: so they hire people who are aligned with the goal of keeping costs down, unlike the American system where hospitals are trying to maximize revenue from all sources.
Meanwhile, private insurers without access to public money will want to keep premiums low, but still claim to provide decent coverage, that will regulate their behavior, especially when they need to prove they're competitive against a non-profit state system.