The thing is though, taxes in the US aren’t any lower, if you include healthcare premiums as “tax”, at least for middle class people.
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.