I don't think this will make parents stop worrying about their kids being grabbed by strange men, and the danger will be just as present as before.
The other thing nobody wants to talk about is that it's not always adult creepy men approaching kids, it's the kids themselves that seek out sexual conversations with strangers on the internet.
Sure, this is also the parents responsibility. But even with open phone access, internet filters, etc they will find a way, especially if their school gives them laptops and there's open wifi everywhere.
That's where this is also for. Parents cannot monitor all their children's internet access at all times. Children will resist and find ways around parents' control, as it has always been.