You don’t need to speculate about feasibility- models for privatised healthcare exist, and it is plenty cost effective in places like Australia and Singapore.
What you’re saying isn’t really borne out by the evidence- at least if you’re not talking about some hypothetical entirely unregulated market, in which case you invite pretty much the same problems all unregulated markets can face, and in gameplay terms cliff assumes away a lot of those problems as being dealt with in the fairly standard manner of most countries. Healthcare isn’t (uniquely) shitty, and honestly the policies which solve the problems arising from private ownership would be pretty boilerplate, which doesn’t make for an interesting game. Same reason we don’t get really any policies that address the problems stemming from public healthcare (such as people going to the doctors for a cold).
Tl;dr I’m not sure the finer points of how to privatise healthcare well are significant or interesting enough (or unique enough to healthcare) to warrant their explicit inclusion.