If they so choose, yes. It is normal.
If said 16-year-old is so close to being an adult, she'd choose to do these things anyway and not get bad grades or mess up. Instead, she sounds like a normal 16-year-old who is NOT "close to being an adult," so her parents choose to follow-up with consequences.
If said 16-year-old thinks it's so unfair, she can get a full time job on top of school and pay for her own phone, coverage, WiFi, laptop, rent, utilities, food, insurance, etc.