Not all but a lot. It is a mixed bag though, Iridium and Thuraya are illegal in India but Inmarsat has a license, so it kind of depends really.

You need a local license because radio frequency is considered a national resource, so each country owns the radio space about its land and they get to govern it.

That makes sense. So the ITU has more of a role of coordination than of actual assignment, I suppose?

Practically, satellites won't switch frequencies every time their spot beam footprints cross national boundaries, so I suppose it's more of a matter of allowing/not allowing service in a given country (as determined by either the mobile or the satellite?).

The other tool is simply not allowing receivers to sold or used to decode/decrypt forbidden sources in a country enforced with import ban like with satellite phones etc.

That's news to me! Does ITU have any ability to mandate laws for the physical spectrum? If not, a global communications committee would still be needed. At minimum, they would need the ability to control the 5G blocks of every country participating in the SAT to cell service.

Like most of these international committees, I believe they mostly facilitate agreements between sovereign states; I don't believe they have any legislative power themselves.

Maybe an analogy would be ICAO's (another "specialized agency of the UN") "Freedoms of the Air" [1] – they define the terminology, but it's still up to individual (or blocs of) nation states to actually grant them to each other, ratify recommendations etc.

[1] https://www.icao.int/pages/freedomsair.aspx