Do the arguments of Kenneth Arrow and William Baumol forclose Market solution provison of health care

The overly long tittle  refers to Kenneth Arrow's information asymmetry argument against fee for service in health care? Does "Baumol's Cost Disease" lead to the conclusion that health care must be paid for by the goverment through taxes?

In regard to Baumol's disease, it is far from the case that his formulation is unchallenged. Baumol makes a number of simplifying assumptions and aggregations in his model most of which have been seriously critiqued. For example see here for an excellent detailed economic  analysis of his assumptions and his logic and analysis. But as usual the headlines are on page one and the clarifications and retraction are found buried much deeper in the paper in smaller type .