They can only offer Internet in Iran with the (implicit) blessing of large nations.
The specific act of offering Iran may or may not help China, but it clearly undermines Russia and helps the US.
Regardless of that, unauthorized deployment of uncensored Internet is a strong political weapon that is only available to large / wealthy nations.
(Contrast this to some sort of hypothetical censor-resistent NNTP style news source, where cheap devices sync the news with each other via local wireless connections.)
I see your general point, though it seems to me to make a slightly-too-strong connection between the US Gov't and its policies and interests and Starlink's (that said, if the two were fundamentally at odds it doesn't seem like Starlink would be offering to provide access to Iranians...)
Let's say it's not even the explicit, Musk just suddenly struggles to find suppliers for his factories in China and his deals to buy raw resources in China start to get delayed.
More realistically, they'd be more subtle. Perhaps Tesla would hit supply chain issues at exactly the wrong time, or they'd announce an extra $100b investment in industries directly competing with Musk's companies. Tariffs are also a thing. They could simply adjust them (up or down).
If you have a working model of how it can be done without global nuclear war, there's probably a Nobel prize waiting for you. Extra credit if you can avoid knocking out every other satellite in LEO and the space stations.