I will be very bold and predict that Trump will bring in socialized medicine, though it will not be called that. Even I do not think this likely, but most do not think it possible, so I still come off as being bold, though some will say insane.
Trump is pragmatic and has shown he is not bound by ideologies. I can't imagine how healthcare could work via competition among insurance companies when healthy persons can opt out. Obamacare, though it will surely crash of its own weight, has planted the notion, accepted everywhere else, that everyone deserves access to healthcare. Trump himself seems to embrace the idea. He may take the bull by the horns, figure he can craft a system that incorporates the private sector better than any Democrat can, for they distrust the private sector, and charge ahead.
It will be a very hard sell. He will lose many of his own people, but may gain from the other side. Even then it may be doomed. Americans are used to Cadillac treatment, and while universal health care is universal, its quality goes down. Pharma too, may scream, because they are used to soaking Americans to offset the modest profits they must take elsewhere. They will carry on about 'choking innovation,' and so forth. As it is, they don't bother innovating unless they see a substantial buck in it; that's why there is MRSA with no new antibiotics to fight it. It's hard to be overconfident here, but I can imagine Trump may try tackling it.
Maybe he can still sell it. Overall healthcare quality in America is well above that of any third world country. But among the developed countries, it comes in dead last. I'm tired of playing Russian Roulette with my modest net worth for every sliver I have removed. Perhaps other people are, too.