Nikki Haley and Kasich should attend if they want further political office aspirations.
Voters don't forget.
What can Kasich run for exactly? He's term limited in Ohio. He's already been in Congress. Other than POTUS, what could his next step be? And forget about POTUS, he won one (1) state in 2016 -- his own. Trump will be forgotten about if you're talking about a cabinet post in a Republican 2020 administration (assuming Trump loses this cycle). And cabinet posts aren't exactly elected. Is it illegal to go back?
He could run for Senate in 2018. If Tiberi runs for higher office in 2018, he could run for that old House seat. As for Presidential runs, Dole 1988 only won five states but he won in 1996. MCain 2000 only won seven and he won in 2008. If Kasich runs again in 2020, he will have a veteran campaign organization and high name recognition for a good early peformance.
He should just do what Clinton did, let his term limit run out, go out on a high note (unlike Hillary going out on Benghazi, not that she could control that...) and spend the next year or so astroturfing, going on talk shows and doing a book tour, writing editorials to major newspapers, getting yourself invited as an expert to various things, etc. then when you run for president you'll start out with high name recognition and favorables.