I suspect he was simply being told exactly what to say by someone in the tower. Don't really see the problem, you can tell from the pilots' responses that they knew roughly what was going on.
On the one hand, I agree with you. No harm was done. The outcry is way overblown. But then on the other hand, the place this controller brought his child deals with many peoples lives daily, and it is really no place for children as an emergency that requires the controllers undivided attention can occur at any moment.
I think the mistake was allowing them to bring the child into the control tower. Once that mistake was made, the rest was handled well. But I don't think either should be fired over the incident. It is a good learning moment. Both (controller and supervisor) should get reprimanded, and the rules made clear about letting children in the tower, but that is all.
That no harm came from the incident means we can laugh at it now (I am sure if I was in one of the planes and found out, I would not be laughing yet).