I think people who are already sick should be covered by a kind of charity (or social services). It doesn't make sense to ask insurance companies to insure people who are already sick.
Otherwise, the socialised version already exists, in most industrialised countries, in some form or another. Within the US, Medicare for the elderly, Medicaid for the poor and children, and in many states, "high risk pools" which are state managed.
More generally, a problem is that the bulk of health benefits do _not_ accrue from direct or acute medical treatment, but from public health and preventive measures, _especially_ well-mother, well-baby, early childhood, municipal sanitation and environmental measures, and general (workplace and elsewhere) safety provisions. Insurance companies of and by themselves don't address much of this.