The great appeal of Single Payer is its simplicity. Like the man said:
Your friends, they don't like you very much anymore. You force them to make too many decisions. With me, only one decision: do what I say.
The more extreme versions of Single Payer would even outlaw spending in supplemental insurance, under the delusion that health care should be completely independent of income or wealth. (For instance, the AARP has a sign on Colorado Blvd. claiming that it's time for "universal coverage and financial security for everyone." As though the two were the same, and either achievable.)
Despite pretensions to morality, this is in fact a deeply immoral vision of health care. It says that it's perfectly ok to spend your money to protect yourself from a home invader, but not from cancer or heart disease or a broken leg.
The notion derives directly from the definition (and abuse) of the concept of a "public good," but that's for another post.