^ A big problem with socialized insurance is pay, though. Doctors are (or were) salary capped in the NHS in Britain, for instance. I haven't checked on it lately but it was like 1% raises or something several years back.
A mixed system with insurance and pharmaceutical companies being heavily regulated would be the best scenario for Americans. Reduce costs without affecting the labor market, cap the price of commonly used drugs, disable insurance and pharmaceutical companies from price gouging, bring back the mandate so older patients are subsidized, while allowing clients/patients to choose which insurance companies offer the best benefits for cost for their specific needs.
Would it shrink the amount of viable insurance companies? Likely, but the free market is only ing us and hard right now. There's a vast shortage of healthcare personnel of every important (read: requiring an education/board certification) type. Doctors and nurses are in critical shortage, for instance. Unregulated (or low-regulated, I should say) healthcare en ies are passing many doctor-like responsibilities to mid-level providers like PAs and NPs to help counter this, but it's not a sustainable model since those are short supply as well.