Same powers a cop has when he pulls you over for speeding. Usually you get the ticket but sometimes you get a warning.
No situation is 100% cut and dried. If the OP had cut off the phone on the first warning, they'd have continued on their flight. But there was the announcement, and two FA's instructing them to shut it off. Often, the plane is not going to move until the passenger complies.
Be thankful you weren't arrested, or smacked by other passengers being delayed by your selfishness.
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