This question is dumb to begin with.
Like, what 16 year old is going to come to their mom or dad and be like; "Yo, do you mind if I f**ck this (guy/girl)"?
I think it should require a written consent from the parent, properly verified by the county clerk.
It should be illegal for a parent to “not allow” their 16 year old to have sex. Fine the parent $1000 if they object or attempt to enforce this on them.
We need to go to extreme measures to reject the nanny state and the culture that perpetuates it, not the opposite direction.
You are literally proposing a nanny state. It's just that you want to nanny the parents instead of the children.