and he said he believes it is a proper role for government to provide a safety-net, with both state and national contributions. “We don’t want to leave anybody out of getting health insurance coverage,” he said.
This was Cain's answer to the question of "pre-existing condition" coverage. Unfortunately, the issue of pre-existing conditions is in fact the elephant in the room for health care reform. It's the whole reason you need a health care mandate -- if you are going to provide a "safety net" which allows anybody to get insurance at any time when they need it, you have to do a mandate, or else everybody drops their insurance coverage until they get sick.
Setting up a government program to provide this "safety net", with the parameter Herman Cain gives: "We don't want to leave anybody out" simply means that everybody can drop their health care, and government will be the new single-provider-insurance for everybody.
Trash Romneycare all you want, and I know we all want to -- but it's the natural result of government trying to meet the condition Herman Cain set in his answer -- "don't want to leave anybody out".
I don't think ANY of our candidates have the guts to say "Yes, we want to leave people out". But if you don't want a mandate, and you don't want government to take over your health insurance, you need to be willing to let people suffer the consequences of their actions. And that suffering has to be severe enough to convince people to buy health insurance if they are not rich enough to self-insure.
Your conclusion does not follow necessarily from the premise. It's certainly a possibility, but you might cut Cain some slack (then again, maybe you don't want to). There are other ways by which people could be helped besides single-payer insurance.