I would suggest that, given the REALITY of our current age, in the long run, it really won't make a dime's worth of difference who controls the state, or kingdom, or protectorate, or what have you.
There were successes and disasters in various forms, since Apostolic times. But those are long gone, kaput, fini - both good and bad.
Wherever the Church was upright, pious and convincing, enough of the population managed to at least respect that and people, generally speaking, were better off, in many cases politically, as well as spiritually and morally.
But man is still man and free will is a cast iron *****. Period.
Anyone counting on a long succession of wise, holy popes, devout bishops and respectful civilians, no matter what form of governance obtains in any particular instance, is setting himself up for massive disappointment. It would take generations to clean out the Augean stables of Vatican politics (much of it held over from centuries before) even if a Catholic pope, a real Saint, were to take the reins in his hand tomorrow.
But if even that assessment is too pessimistic, the other half of the problem is governance in a time of metastasizing nuclear weapons' and delivery systems' technology, law by executive fiat usurping the constitutional republic, massive economic instability and balkanization.
The whirlwind has already picked everyone and everything up and where we shall finally crash land is anyone's guess.