I don't think your methodology of looking at global plans holds up, because on balance those are a self-selected crowd (a bias, likely toward healthier people) and if you note that the standard of care is different, the price is going to be different. These healthcare companies know what product they are selling well.

I think it's clear that there's significant waste in terms of advertising, haggling with each other, etc. that you don't get in a universal healthcare system. However, there is also waste in universal healthcare systems around the cost of the bureaucracy to manage the leviathan.