You don't need to shut down the internet to find Starlink users. Starlink dishes are not passive. You can easily detect them with SIGNIT vehicles. This concept is as old as 1980s. Also, the IR has a history of shutting down the internet when protests happen. They did that in Aban 98 and during Mahsa Amini protests. Starlink didn't even exist in Iran then. So, try again.
Millions of Iranians, including me, would rather see Iran balkanized than to live with the Mullahs who want to give Iran to Iraqis, Lebanese and Palestinians. I would happily live in a land-locked Tehran if it means that not even a single penny of my resources will be spent on Arabs who hate Iran with a passion. And I'm sure millions of Iranians share that sentiment. Whoever will be installed, even Maryam Rajavi, will be better than Khamenei and his thugs for sure.
The period of scaring people about Balkanization is over. The Islamic Republic is by far the biggest threat to Iran's territorial integrity and national security.