Government health insurance doesn’t destroy private insurance or the ability to pay out of pocket. You can still get private healthcare in countries with national health systems.
Also, for most americans, your only option for insurance is what your company offers. You may have access to multiple policies; you may not. Generally the better off you are, the more likely you are to have access to multiple policies or to policies that cover more. But it’s not like your average american is shopping around to find the policy that best suits their needs out of the entire market.