> it will be forced to go through local servers to operate legally.
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.