Other point I would like to make is that our healthcare is not “free”. It’s paid by high taxes be are obligated to pay to the government (the taxes are as high that I don’t even want to know the exact amount in my case but is around 25-30% of my salary).
I'd imagine that most people would stay signed on but it does give people who either distrust public institutions or just don't feel like they would benefit from a public option a choice.
Full disclosure: I am firmly on the side of socialised medicine.
It's considered political suicide to even openly discuss dismantling the NHS which is why even the Tories continue to tip toe around the issue even after having been in control of government for more than a decade at this point.