Kristol's possible entrance in the primary has the possibility of weakening the Republican side and opening up the possibility of a Democrat candidate winning the presidency. This is something that would be catastrophic.
His 2018 tour seems designed to argue a challenge could work, even if one never quite has. (Notably, the party in power lost the White House in 1968, 1976, and 1980.)
“If I could just shake people up a little bit,” Kristol told BuzzFeed News after the Saint Anselm remarks. “Get them out of ‘Gee, I just saw a poll where he’s got 82% approval among Republicans, it’s over.’ If I get them to think for a minute, I think that by itself is useful.”
He wondered hopefully, in the interview, about the availability of Mitt Romney, Ben Sasse, and James Mattis — three men who were on his 2016 wish list — and of Nikki Haley, who like Mattis ended up taking a job in the Trump administration. Kristol also has kind words for John Kasich, whom he visited recently in Ohio and acknowledged is the Republican most likely to take on Trump, though the governor’s personality and moderate politics have turned off other leaders in Kristol’s neoconservative orbit.