This should not then be measured by health outcomes, but economic!
It's quite plausible that health outcomes would be similar in aggregate. If you need urgent expensive surgery that takes your home deposit, you'll still pay it and live if you have no other option.
I'm not sure if this answers your question - but in general I don't believe health care should just be about preventing death.
I think doctors get a lot of credit for reversion to the mean.
But in many countries insurance seems to work like a subscription service that covers everything including things that have a 100% probability of happening (like common cold).
Quite naturally, the people who are already paying for it would want to go to the doctor's office and the people who would have to pay for it out of pocket, would not.