well you need to in a public system that's overloaded, so you lose both when paying in and again when you need to get treatment.
E.g. the UK NHS costs less per capita than Medicare + Medicaid costs per capita (not per user), despite the former providing universal service. Partly explained by artificial restrictions on Medicare limiting their ability to negotiate price - the "free" market is intentionally prevented from functioning. It's pretty much corporate welfare paid for by regular tax payers. I never understand why Americans tolerate this.
The proportion who pays twice in the UK is around 10% who opt for private insurance on top. The proportion who pays twice in the US is every tax payer.
Total healthcare spend per capita (public + private) tells a pretty clear picture, where costs of healthcare in the US is totally out of control.
The US system is designed to be profitable for those running it, not offer good value for those using it.