This is a non event that gets blown out of proportion by the media as usual.
The clearance itself issued by the kid, or the frequency change... that's nothing to do with the safety of those actions. The safety comes from the thinking behind the clearance. And that was obviously done by the father. A synthesised voice could issue the clearance for that matter.
The problem is just one of professionalism and "etiquette". Not of safety. Also bear in mind that the father was probably plugged in via a mentor socket which automatically overrides the "trainee" one, if anything went wrong.
You could compare this to turning up at Borders and Immigration. A kid takes your passport, passes it on to his dad standing behind, he checks it and gives it back to the kid who hands it to you and lets you through.
Not a safety issue, but most people still would find this unprofessional.
Same kind of thing here at JFK I would say.