Uhh, the US has had extreme government regulations regarding healthcare for as far back as I remember. Every state has it's own insurance administrator and purchasing insurance across state lines isn't allowed. What we have right now is the worse of both systems actually. It's a heavily regulated false free market where the customer has basis for comparing prices and has no direct control over providers. Instead they must choose between a government chosen option or an employer chosen one. It's just terrible all around.
With a single payer system, at least it would be fair to lay all blame on the single payer. It'd still be beuqacratic and political, but at least there'd be direct responsibility.
Removing the regulations, at least the customer would be able to choose a provider themselves and people could sue over pricing disagreements. There would be issues with pre-existing conditions and low income that would still need to be addressed, though.
Either option is better than where we are today, which is, well I'm not sure. There's not really a term to define the mess we've created. It's not socialist, it's not capitalist, it's just a mess of special interests, political concessions, and reactionary legislation. I guess the one thing we can definitely call it is bureaucratic.