With the exception of the current US administration, hostile countries and corporations try to appear non-hostile when possible.
The President, within this context, identifies a single entity. As such, it is a proper noun.
Analogy: there are many continents. But if we're discussing Brexit, the Continent is a proper noun. I don't think it's incorrect to not capitalise. But it's certainly gramatically okay, and not in the same bucket as The Nutters who capitalise Random words it Looks like Legalese.
I have an internal convention to not capitalise LLMs when talking about them as if they were people; so claude is not capitalised, and the internal LLM-based service agent we're building, rex, is not capitalised.
I realise this breaks the capitalisation of proper nouns; claude is a name and therefore a proper noun and therefore should be capitalised. But I like that there's a signal in here that the thing I'm talking about is not a person and so we don't capitalise the name (I realise that cities or companies or other things that we capitalise are also not people).
Digression, but then so was the entire discussion on capitalisation.