The UK is not a good example - it has a fairly unique nationalized system.
Germany, on the other hand, has a regional and national market system with compulsive health insurance, much like the ACA attempted. It's not a public only system by any means.
It's not about sharing a room, actually. It's about reducing the burden on the state, providing more efficient service for cost for everyone.
In Germany, it is about comfort. The public insurance is achieved via competing entities, but those are not-for-profit organizations. It's safe to say that there's no health benefit whatsoever of having private insurance in Germany. It's just nice and you can feel good getting quick appointments with any doctor you like. Necessary treatments are free for anyone else as well.
Hospitals in the US are also non-profits. Many insurers used to be as well.
The difference really is in who negotiates. In the US, it is usually individuals organizations or companies - in Germany it is mostly the state, though people still have choice. It's not administrated by the state, though - it's administrated through public/private partnership. Personally, I think it's a great system, and I wish the US would have implemented a version of it more successfully.
Germany, on the other hand, has a regional and national market system with compulsive health insurance, much like the ACA attempted. It's not a public only system by any means.
It's not about sharing a room, actually. It's about reducing the burden on the state, providing more efficient service for cost for everyone.
Further, the main issue with public-only systems is wait times. In Canada now the wait times are extremely long - in the area of 20+ weeks. http://www.ctvnews.ca/health/healthcare-wait-times-hit-20-we...
That's not about comfort, it's about getting treatment.