A Republican solution which used market solutions where they would work within the Obamacare framework would likely be a far better model than anything proposed thus far. Instead of attacking the whole, they should improve the parts.
Of course, markets only work within a rules-based framework, so if there are regulatory shortcomings, those also need to be addressed.
The heavy price rises are the big problem. There's no reason to suppose they are intrinsic to the architecture of Obamacare. Indeed, Obamacare held costs down at first where the premium growth curve was out of control in the previous model - premium growth also delivered a system of declining coverage (50m uninsured) and widespread health-related bankruptcies.
Finding the cause of premium growth and sorting them out is dull work. It's much easier to use pejorative labels. But broad coverage is popular and large populations can usually extract economies of scale.
Sadly, these Republicans won't do this because they despise the vulnerable (programs for the vulnerable are labelled "entitlements" so thoughtless people can avoid understanding the groups of elderly, sick, handicapped, mentally ill and other unfortunate people they are harming) and their great desire is to give a tax cut to the rich. They are the EVIL party for a reason.
I suppose Republican assume that Democrats aren't the least bit concerned by freeloaders. But many actually are. The key is to minimize the number of such people without damaging those who are genuinely vulnerable.
I am pretty sure there are (or used to be) Republicans who are actually concerned to make sure the vulnerable aren't harmed, while nevertheless wanting to advantage those who work hard.
My view is that this is where the end solution to the political impasse lies. At the moment the hard ideologues rule. But people of goodwill will break the logjam in the end.