Both of my kids worked in high school. Neither worked their freshman year of college. Now my daughter is working in a graduate assistantship in her field, my son is playing baseball. She gets paid, he gets tuition help. I consider both of them investing in their chosen careers.
We raised them both to be very independent. They don't call for things like "i have a problem with this teacher or this coach." But they do call. They ask things like "what should I do with my kitten when I'm having a party this weekend?" "My wallet was just stolen, what do I do?"
Parent always will have a role in raising their kids. I still call my dad for advice and I'm 50-plus. The trick is to find the appropriate role at each stage of their lives.