" Such a meeting would be about be about coopting each other for political advantage, not for promoting the Kingdom."

Indeed, this entire little tempest is highly political, and in no way for "promoting the Kingdom." If the pope does not meet with the evangelicals whom his personal propagandists attack, they come out in the high side for at least asking. If he does meet with them, they still come out ahead for seeming to take the lead in healing a culture war that has spilled into the spiritual realm. So on the PR front this is a win-win for the evangelicals. On the religious front, it's just another day in the life of the culture wars which ultimately are about personal morality.