What is it meant to achieve?
Is it supposed to be a warning to other parents - make sure your kids behave or end up in jail? Would that even work? Not sure. It must be a tiny minority of parents who actively cause delinquent behaviour in children, and of those, some of them might actively be choosing not to parent, but some of them will just be completely clueless/struggling heavily with multiple issues of their own, so not sure that it would be much of a deterrent, since someone with that many issues is unlikely to even notice much outside of their own immediate experience.
Is it meant to protect the parents' other children? Because sometimes parents who have one delinquent child have other children who behave perfectly normally, who are probably already suffering/struggling due to their sibling's behaviour. The impact upon them on being removed and taken into care because their parents have been prosecuted would be massive. That kind of trauma may well lead to the same kinds of behaviour that you're hoping to avoid in them in the first place.
If the parents do have other children that they are similarly failing then it might be helpful in that scenario - but again, if you're hoping to help those children not become delinquent themselves, then it might be worth looking at whether prosecuting the parents (and therefore removing the kids) is the best course of action, or whether that might be likely to cause more issues in the kids, or whether supporting the parents might be better for the children.
What about children who are not brought up by their parents? Or who are brought up by a single parent? What happens in that scenario?
I can see the thought process of the surface idea, but I think you have to go back a step - what's the situation now, what should it be, how to achieve that.
I assume you're saying
Situation now: Poor parenting is causing teenage crime
Situation should be: (More/most) parents should parent effectively, therefore preventing/reducing crime
Way to achieve: Punish parents whose children commit crimes
So I think if you're going there you've got to go back to the root of what the situation is now and examine that as a premise. Is it poor parenting which causes teenage crime? Is that the only cause? The main cause? Can we define/agree on what "poor parenting" consists of? Why might parents act in that way? What might help them parent differently?