The current healthcare system was mostly shaped by Democrats with the Affordable Care Act (sometimes called Obamacare) at a time when Democrats held a filibuster proof majority.
The ACA is grounded in a lot of political policy going back to the Nixon era, and draws from quite a bit of conservative ideas. The individual mandate itself, for example, was a Heritage Foundation proposal from the late 80s, and was ironically one of the main targets of Republican objection during and after the implementation of the ACA.
The ACA is, in fact, warmed over RomneyCare(tm) (a Republican, please note) from Massachusetts.
The fact that Kentuckians loved Kynect and hated Obamacare--which are the exact same thing (aka the ACA)--tells you everything you need to know about the Republican voting public.
Additionally, the fact that Democrats took a pro-corporate conservative policy package and rebranded it speaks volumes about how much daylight actually exists between the parties when you ignore the culture war rag waving.
You call that "the uniparty", while other here at the same time say they want less polarisation and more bipartisan consensus.
Make up your mind.
(I am old enough to remember that Obama convinced the Democrats that it was better than the existing system, and that small progress was better than keeping the status quo or waiting another decade to have maybe, someday the numbers to pass a better bill)
If you review Nixon's CHIP proposal (https://www.nixonfoundation.org/2015/11/the-nixon-comprehens...), you'll find a proposal that maps pretty closely onto the ACA marketplace that we now have available.
"Mostly shaped by Democrats with major proposals cribbed from Republicans" would be a more accurate assessment.