Jared, I think your analysis is missing a critical element. The corporate "profit-motive" isn't to blame here. There's something more fundamental at work.
Only 20% to 25% of health care delivery in the U.S. comes from for-profit corporations (https://www.ncbi.nlm.nih.gov/books/NBK217897/). The bulk is delivered by non for profit corporations that should, by definition, not respond to the profit motive. So, our current lousy situation results from a predominantly non-profit delivery model.
How can this be?
Healthcare is fundamentally driven by a conflict between existential demand and social cost. On one hand, we want policies, practices and standards that decrease the social cost of healthcare delivery. On the other, if an immediate medical situation threatens our life or the lives of those we love, most of us want the best possible care no matter the cost.
The result is a system with an insatiable appetite for consuming as much as possible. Contstrained supply with infinite demand always creates problems.
This understandable human paradox informs much of the dysfunction in the health care system. We delude ourselves when we think that the profit motive isn't at work in non-profit corporations. To be sure, the corporation isn't beholding to stockholders or owners. But it's beholding to board members and the financial pressures of staff that are, individually, for-profit entities, therefore subject to the same supply/demand pressures in the marketplace as their counterparts working in the for-profit sector.
Ultimately, there is no solution to existential problems like these. There are ethical choices that can help balance the conflict. Still, any dollars sourced by taxing the rich and eliminating for-profit healthcare will simply find their way into the pockets of bureaucrats, lawyers, administrators, and providers who believe they deserve a bigger share of the pie because they are paid less than the person in the next office.
Non-profits are also good at diverting excess capital created by excess "profit" and charitable contributions into reserves that generate unrelated income.
A strong balance sheet makes for a more sustainable organisation, but it doesn't reduce the cost of delivery in the short term. Again, another paradox.
Ultimately, we are all our own for-profit corporations that want to both live another day and be paid what we "deserve" (always more). I've worked in for-profit, non-profit and government sectors and in my opinion they are equally flawed reflecting the reality that they are all a container for flawed humans.
This problem sits in the category of "beware what you wish for". Until we have the humility to admit there is no easy solution we will not be able to find a more reasonable path forward.