Whether it's Kasich or somebody else, those who oppose Trump need to unite behind a single candidate. Trump won the nomination in part because the field was so crowded (and Trump stood out as a novelty).
The Republican party isn't what it was in Reagan's day; an old Reagan hand like Kasich probably isn't what the primary voters want. Kasich is, I think, building towards making an independent run, perhaps matched with a veep like Hickenlooper from the ranks of Democratic governors. His appeal will be to that swath of independents who are more conservative on economic issues and more liberal on social issues, and who value competency. The Trump years, whatever their ultimate outcome, are marked by chaos and extreme partisanship. The appeal of a Kasich/Hickenlooper ticket is essentially non-ideological and rooted in a desire for replacing the current model of politics-as-bloodsport.
Kasich isn't what the voters want; that was very obvious in the primaries. The voters didn't want an establishment candidate nor a RINO. That message couldn't have been more clear. He only won his own state. If he had the appeal that you think he does, he would be sitting in the oval office. That appeal didn't surface through the entire primary except in OH. Yes, the playing field was quite large, but there were only two that appealed to the voters; both of them anti-establishment in their views and only one was from outside the beltway. The voters obviously selected the one outside the beltway. Like him or not, Trump was victorious in defeating Clinton in an upset that the left never saw coming, nor did they think was possible. Even the GOP establishment was taken by surprise.
As for the Trump years, I question how you can make such a statement that it is marked by chaos and partisanship. For starters, last time I checked the Trump years aren't over, they are just beginning. The chaos has in large part been created by the MSM, the DEMS and the leftists who still can't get over the fact that the 'Queen of Liberalism" lost. The liberal leftist mental midgets have become increasingly ugly. The GOP's partisanship has been ongoing for years, because of RINO's like Kasich. Kasich may very well run as an independent but the results will again be defeat, if only for the simple fact that it is nearly impossible to win as an independent. The fact that he has proclaimed to be a Republican all these years and then run as an independent and run with a DEM as you seem to think likely, to me spells out immediate defeat and quite frankly, makes him a joke. Clearly, being in politics as long as he has, he knows that he has almost a zero chance of winning as an independent. So, other than siphoning votes (to whomever he's targeting) what would be his objective to run as an independent? Rant and rave with like another 'Crazy Bernie' with his arms a flailing? Quite frankly, I hope he does run again and when he loses, his political career will be over and conservatives will have one less RINO to contend with.
