Yes we do have a big private health service in Britain Vish mainly rich people and corporate. Most big companies put their management staff in private health schemes however you are taxed on it as a benefit in kind. The same consultant doctors as work in the NHS also work in the private sector and earn huge amounts of money. For some operations like say a new hip you can wait years on the NHS whereas if you have private insurance you can be treated immediately
It's the same here, except that up to a limit the contribution to health insurance is deductible in our tax calculation. But, those not having the means go to the public hospitals which is much much better than not going because you cannot afford. As I said, even Trump had to change his strong views with free tests and treatment, hopefully the americans would see the need as a society of having free health treatment now even if it is the wealthier who pay through taxes.