My asexual daughter (really, not my fantasy - its her identification - at least currently) is on birth control. Evens out moods, she doesn’t worry about a period anymore - and the crampy feelings that go with it, and clears up acne. Plus, if she would have sex - with someone with a penis - she’d be protected against pregnancy.
Pregnancy is a big concern for parents. As are STDS. As is sexual violence. As is having your heart broken at sixteen. The last happens if you are straight or not. Sex adds a layer of complications to teenage relationships - which are hormone heavy and drama prone to start with. I think most parents would like to delay their kids having any kind of sex for as long as possible - sensible parents recognize there is little they can do. Sensible parents realize that you still worry.
I’m more worried about my son. He doesn’t like to tell us what is going on in his life. I’ve met one girlfriend - I don’t know if he has had others. He could end up getting a girl pregnant and we might not find out about it for a long time. If he penis turned green, I’m not sure he’d tell me - much less tell me about something more subtle.