For one thing, healthcare is such a mess in the US that it actually might be easier to just nationalize it rather than trying to fix the private insurance system.
Also, in a country with both, the private system can't be any worse than the public system because it has to compete with it, so the fact that the UK has good private healthcare doesn't necessarily mean that it will be easy to fix the private system in the US without the existence of a nationalized system as well.
Also, in a country with both, the private system can't be any worse than the public system because it has to compete with it, so the fact that the UK has good private healthcare doesn't necessarily mean that it will be easy to fix the private system in the US without the existence of a nationalized system as well.