As long as government controls the country, it's the country as a whole. Because that's where the government gets its resources.

That's just not true. You don't know what you're talking about.

I encourage you to skim through the sanctions. I promise you that you will find plenty of exemptions telling you not to block every Iranian citizen from communicating, not to block them access to information, not to block them from free-to-use services, not to prevent them from traveling etc etc.

If you just cut the whole country off the internet, how do you expect them to organise towards overthrowing the government? Via carrier pigeons?