The USPS is probably the best postal service in any large nation. So if the USPS is any guide, we will at least have the most efficient socialized medicine in the whole world.
Which still means it will suck, but it will just suck less?
Health care is a much gnarlier animal than letter and package delivery to manage. The general principle seems to be the larger the population covered, the more unmanageable and grief ridden the socialized health system is. This is why Sweden beats out Britain’s NHS for example.