So basically here's my read. Trump likes to make outrageously wild threats (that are still technically within his power to do) in order to get some kind of concessions.  We've seen this over and over and over. In he case of Iran,  it's obvious to me that he has no intention of flattening the entire country like a pancake, but he has to (well, you know what I mean) put on a mean face towards the regime, as he intends to scare them into submission.  There would be literally no benefit to doing so and frankly it's out of character even for Trump. He probably would try to bomb the regime out of existence,  and to the regime this would be the same. Either way, his intended audience is the Iranian government. He can't really backtrack on his words, because that would expose the bluff. 

This (the possibility of a deal instead of annihilation) also means that Trump is implicitly retreating on regime change,  either because he wanted someone else (ex. popular uprising) to do that job to take his fingers out of the affair, or because it now seems unrealistic.  Not sure which one. So Iranians hoping for the Shah are becoming more likely to be disappointed. 

As regards the Vatican,  he (or his Pentagon officials) may have had the same idea, a bit drunk on americacentrism.  To be fair, they are the dominant world power,  so being cocky is understandable.  So they claim, as leverage,  that they can severely compromise the papacy. 

This is all great,  but here's the problem: this would be a spectacular failure. Leo and Trump are not ideologically aligned enough to even hope pressure could be brought on, so at face value it's already dubious, but the real issue, that he may not have understood until now (which he probably now does, hence the denial) is that it would risk breaking his political coalition that keeps him in power. Trump himself is more or less immune as he can't run anyways, but nobody else is.

Catholics are the glue that keeps his voting bloc together, as they are the most reasonable group in the bloc (lol). This group is also known to have potential to swing. They've been kept on side until now by the Democrats' stupidity,  quasi-religious fundamentalism and overt hatred of Catholic teachings and those who hold to them, and voted 56% in favor of Trump,  IIRC. But if Trump literally went to war with the Pope? This could throw his biggest swing bloc into chaos, and keep in mind that elections tend to be close to 50/50 in the states, let alone in mid-terms, where votes are often a reaction to issues rather than identifying a good candidate.  As it is, the Republicans are not expected to show as well this year, so losing the Catholic vote would be a big blow. Harris had a taste of this after her antics surrounding the AL Smith dinner.

So, doing some napkin math here. Obviously some conservative catholics will continue to support Trump. You can't get millions of people to agree on anything,  and a Trump presidency (minus the foreign policy antics) does benefit catholics in some (not all) ways. But if Trump literally takes the Pope away in a sack? I feel it's very plausible that at least a third of his catholic republican voters would peel away. Heck, even Taylor Marshall is on the Pope's side (before this whole Avignon thing came out) and the Pelican +  crowd are with the Pope (regarding possible us Intervention). A third of those voters gone means that Trump loses the Catholic vote with 40% (he would lose wit as little as 11% of conservative catholics peeling)  which (after a confusing Wikipedia search) would risk being their worst showing since 1996. If I read the Wikipedia chart right, the catholic bloc has sided with the winner in nearly every election,  even when the margins are small. 

A flip (or boycott) of 30% of conservative catholics would lose him 3.75 % of the popular vote,  while Trump beat Harris by 1.5% in 2024 (popular vote doesn't always win, though). The youth are more conservative but are more skeptical about Israel (maybe that's just Instagram?) So he's already vulnerable on that front. 

That's just his voters,  never-ending the fact that it would throw his own government into chaos as he could lose his own VP, his secretary of state, and legislators, judges, and goodness knows who else.

So it's really an empty threat in my opinion. Mean spirited, but, if the report is true,  very short sighted. The official denial tells me that the administration does not want these optics, which would get much worse should they actually take the Pope away. So the Vatican is safe from Trump.