But in the end, that is the grand experiment. Do you accept an experiment to prevent your child from getting sick, or do you take the chance of them getting sick? I'd wager that the Delta variant has changed how parents look at that balance equation.
Ignore the "attack" on you, and looking at the big picture- this is honestly a balance between risks, for all of us. So far, the adult data shows that the effectiveness is far better than w/o, assuming the hospital data is accurate. And noting the increase in younger people getting sick, it appears that the same balance will apply to kids.
Now if the 3rd dose reduces the ability to spread the virus, that's really good news. We have to remember the goal of the vaccine was to reduce the need for hospitalization and death. It was never going to be perfect, but considerably higher than w/o. If a 3rd then prevents others from getting infected by a person, that will help the doubters quite a bit- without them actually having to get a vaccine.
That being said- what would be better- the US getting a 3rd dose, or country X getting their first 2? I would suggest the latter.