"Hospitals barely make money as it is, I don't see how this is a sustainable solution. Paying more does not create capacity in this industry."
The problem is – and this may be very bizarre in a society as capitalistic as the US – healthcare should not be beholden to making a profit.
Rehabilitating people is clearly "valuable" to the economy in that without people to participate in the economic system, a debt-based economy collapses; I'd argue that healthcare is much more valuable to capitalism than is reflected on a balance sheet of paper costs/revenues/profits, and yet a system such as ours has absolutely no way in its current form to price that in (sure, in an academic defense you could wave hands that "positive externalities" such as these should be priced in to the model, but it's clear with the racket the medical industry has found itself in that will never happen practically).
The main issue profit-seeking conflicts with is that whole rehabilitating/healing/saving people is an intrinsically good thing to do, and that letting people who have full lives to live die or suffer is an intrinsically bad thing to do.
What's not sustainable is that healthcare has to survive within the confines of a system that is many times in complete opposition to it. Other otherwise-capitalist countries have at least tried to insulate their healthcare industry from market forces, meanwhile the US has just wrapped it in another layer of capitalism with its insurance market.