They should. I'm not sure that they all do.

Around Trump's inauguration, I heard people making the "Trump appointed by God" statement as if he were uniquely appointed by God - as if he was different from Biden and Obama.

Now, that's not Christian theology. The Christian position is as you stated. And second, the "Trump uniquely" thing is (almost certainly) not the position everybody who believes or says that Trump was appointed by God. But the prominent people, the ones being quoted, sure sounded like they believed "Trump uniquely", which is a distinctly non-Christian position.