Almost by definition, a governor can't be an ideological purist. He must lead, address real problems, assemble coalitions. But a governor - especially one whose experience is as all-encompassing as Kasich's - can make a great President, especially if the GOP can retain Congress.
That's the real issue there - if the GOP can regain the Presidency while retaining Congress, the conservative agenda can advance. A nominee like Trump or Cruz will not only lose the White House, but will also be a down-ticket disaster for the rest of the party.
Nominate Kasich, and sunny days are ahead. Nominate Trump or Cruz, and the conservative movement and all its current leverage and influence will be eradicated.