A reasonable assessment - your reference to the Vatican being frustrated by its inability to exert geopolitical influence in favor of the Catholic communities in Israel, Lebanon and Syria is insightful.
I was also thinking about the internalization of Jerusalem under UN auspices. Obviously it will never happen, but the UN still holds on to the idea, that's the underlying reason nations moved their embassies out of Jerusalem. It's one of the prime reasons the Vatican delayed recognizing the State of Israel until the mid 90s. I'm sure the idea, and resentment, still rattles around some Vatican hallways.