This implied dichotomy between "government funds healthcare" and "choose your doctors" is false. Vouchers for private health care would help the poor AND allow the market to encourage good care.
Who here can honestly be in favor of denying healthcare to those who can't afford it?
Everyone. Almost every life could be extended with more money, so at some point in any system you will have to deny healthcare to someone who can't afford it. Only our cutoff points differ, between $0 and "freeze everyone who dies".