While I agree this makes the most sense, the problem is that the GOP establishment has lost control of the party on the base level. Right now the GOP primaries are set up in such a way that southern states have huge impact on the early stages of the process. If a fringe candidate can survive past NH, he or she can overcome the establishment candidate throughout the south. Trump voters aren't going anywhere, nor is anti-immigration sentiment. I can't see Kasich channeling into that, whereas a Ted Cruz...Tom Cotton...or even Trump again will do it easily.
Jeb Bush had the money and connections to win the nomination under normal circumstances. His machine was so powerful he effortlessly boxed out Romney's team, forcing him not to declare for the race. And yet Bush lost, bad. Sure Jeb isn't as talented as his brother but his brand was rejected, not just him as a candidate. Kasich and other "moderates" will face the same problem.
Another thing to consider is the Clinton WH. Assuming Clinton is faced with divided government it's very unlikely she'll accomplish any of her liberal agenda points. Instead she'll be forced to triangulate with republicans early. This type of compromise will further incite the right. At some point in her presidency I'd also expect Clinton to begin issuing major executive orders, most of which will stick unlike Obama's thanks to a reshaped Supreme Court. This will be one of the few ways she can fire up the base, and this will further incite the right. Long story short, I'd expect republicans to do well in 2018 midterms and once again be spiraling down the far right extremism drain.
I think Clinton will be very vulnerable in 2020 and would likely lose under normal circumstances, assuming the economy continues to just get by+Obamacare falters as republicans dither. But nominating a Ted Cruz type could once again provide a boon to democrats. If I was a republican operative I'd be looking around for someone who can appeal to the ugliest facets of the far right while also satisfying the establishment. Scott Walker types. If republicans can't nominate someone impressive like Kasich, their next bet is to nominate someone like Walker (not Walker himself, but someone in that mold). And if they shit the bed again they'll get a Trump/Cruz/etc type.