This is a largely undocumented feature, and you would not be the first person who simply could not get it done. (Note the post from 2019 claiming that this feature has been discontinued.) Does the language appear in the terms of the card that you hold?
So, I have returned after having done some due diligence
I contacted the Amex ICC call center in the UK and was immediately connected to a wonderful representative that truly amazed me with her knowledge of the subject. The ability certainly does still exist, and she made very clear that you are limited to a single transfer in a 12-month period, for all accounts worldwide (the poster who managed to transfer from HK to ICC to U.S. perhaps got lucky). She did confirm that points can be transferred from ICC to the U.S. and vice versa with no problem at all (and surely the same goes for any other country not on the ineligible list).
Also, with regard to a points transfer from Amex Israel to an ICC or American Amex card: it cannot be done. It turns out there is a short list of ineligible countries and (of course) Israel is on it.
Honestly, the fact that I was able to get such a polite, knowledgeable English-speaking agent on the phone in a matter of seconds is almost enough to have me sign up for the card!