If it doesn't, it's possible, through voting, to change how that operates. There's absolutely nothing that can be done in the 'free market' which would have any impact on providers/insurance companies.
The powers are entrenched and voting does little to change anything in government anymore.
We don't have a free market health care system anyway, it's a hodgepodge of regulation and absurdity today. Making it single payer would simplify that situation, but claiming it would add dignity to the process is just uninformed.
I agree with you there in the context of the US. What desperately needs changing is campaign finance. Lobbying, Citizens United, etc has completely ruined politics in the US.