They've got a much easier way of preventing it from operating: Ban sales of Teslas until Musk relents.
Nice factory producing 250k cars per year for the Chinese market you've got there. It'd be a real shame if some sort of party of workers were to seize the means of production.
So as much as it hurts me to say it, I don't think this or anything else will make a difference. Once freedom is lost somewhere, it may not even be possible to get it back.
I do think though that the CIA should at least take advantage of this new technology to undermine hostile foreign governments. Mass produce a few million cheap satellite phones and use balloons to scatter them all over China, North Korea, etc. Even if it doesn't have much practical effect, the overt disrespect will help to undermine our adversaries and force them to expend more resources on tightening internal security controls.
Not having to operate legally is the whole point here. The hope is that Russia / China will have no way of preventing Starling from existing (maybe except shooting down satellites and causing a major international diplomatic incident).
There's still the question of how to make this profitable, if Starling is illegal in Russia / China, it will be difficult for them to interface with their financial infrastructure to receive payments. This could be solved either with cryptocurrencies or support from other governments and human rights organizations. It's also possible that Starlink will allow certain activity free of charge, particularly during protests and internet blackouts.
This moves the global nature of the internet one step further. Until now, it was generally possible for law enforcement to force ISPs to censor content and give up activity logs, something that made catching criminals a lot easier. Satellite networks make that much harder, especially if your government isn't very friendly with the jurisdiction the ISP is incorporated in. It's not unimaginable to me that, in ten years, most black hat US hackers will use a Russian satellite network as an additional layer of protection. Even if all else fails, all their devices get compromised and their IP address leaks, the Russians won't give up the customer info for that address anyway.