The first mistake you make is accepting that the federal government has a role in our private health care.
From there it is just big government statism options on how big government statism can achieve the results you seek. Picking winners and losers based on the "greater good" as viewed by those in power. Our government isn't supposed to be in the position of picking winners and losers. You are in the trees and have lost sight of the forest - a forest you shouldn't be in in the first place.
You fail to appreciate that liberty with respect to our private health care is a function of the rules in place for health care financing. There's no bar - never has been - keeping you from seeing the doctor of your choice. Except for the reality that you'll have to pay him. And for most of us, that depends on the quality of the insurance we have.
Disparities in medical outcomes is a function of the quality of insurance. For many, the current employer-based system continues to work okay, even as copays and cost-sharing seem to go up every year. But an employer-based system has distortions of its own - including tying folks down to jobs they don't necessarily want but hang on to for the insurance. On a macro level, that decreases job mobility and economic growth.
Notice I haven't even mentioned the dirty word "fairness" yet. But this isn't a matter of fairness between rich and poor - I know that as conservatives we can't be in favor of that. It's a matter of fairness between folks lucky enough to have a job that provides health coverage and those who are unlucky. That is, it could be you or me next week, next month, next year, who may be out of one of those lucky jobs and forced to work two part-time gigs with no coverage. And unlucky enough to get sick - because we'll ALL get sick at some point in our lives.
What are the sorts of things that the community typically provides to all and finances through general tax revenues? The common defense, roads, bridges and other infrastructure, Social Security in old age. Things we all use or need, at one time or another, whether we're lucky or unlucky in life.
Same thing with insurance for medical care. Consider the thought experiment posed by John Rawles - if you viewed the matter through a "veil of ignorance", not knowing your circumstances in life, not knowing whether you'd be have a job with health benefits or not, not knowing whether you'd be prone to disease or poor health, not knowing whether you'd have savings to address an unexpected emergency or be left to the mercy of others. What sort of health care financing system would you favor? A system based on the arbitrary circumstance of employment? Or a system based on everyone contributing their fair share to an insurance pool that offers security against arbitrary destitution?
Look, I'm an old man from an era when conservatism wasn't about selfishness. I've been advocating for a private insurance-based alternative to our employer-based system since before Obama entered politics. I supported Romney in part because of Romneycare. Now the ACA has discredited among conservatives the private insurance model for addressing access to affordable coverage, even though the basic idea has a conservative pedigree with its genesis in the Jack Kemp era. I may well be alone in thinking it can still work, and that the ACA's flaws are not fatal.
But the conservatism of my generation is denounced as liberalism these days, and it seems that no one's willing to even listen. But if today's conservatives can't or won't fix the ACA, we need to face reality - the only politically viable alternative may be single payer. Medicare for all, financed by general revenues.