In the US it is a routine procedure to remove wisdom teeth that would be considered healthy and non-problematic elsewhere, even in older adults.
Source: my mother is dentist, and I've known multiple people move to the US and suddenly as a middle aged adult need their wisdom teeth removed.
For some reason Americans are more enthusiastic about unnecessary medical interventions. The pediatric ear tube surgery is another example.
I don't remember having any particular pain or anything beforehand, I was just told I was getting them out. There was no discussion about whether I wanted to do that or not. I had already had braces at that point, and they were causing my teeth to shift again, so maybe that had something to do with it.
Feeling back there with my tongue now, I think there's room for another tooth on each upper side, but there is no room for more on the lower jaw. This makes sense with what I remember being told, that they were 'growing in sideways'. In a scenario like this I wonder if they are concerned about being able to keep those very back teeth clean, in addition to the cosmetic issue with movement of other teeth.
Botox works by blocking neuromuscular signals. As far as I'm aware, wisdom teeth coming in is a bone-tooth interaction. Botox would do nothing.
Maybe botox would do nothing. Maybe it would disrupt further development of the tooth.
Of course, I'm far from an expert in anything related to medicine and I'm sure there's some reason this is dangerous/wouldn't work but I'd love to know why...
You're framing this as if it's a mortal sin to administer medicine to children. Botox is well studied. If there is medical benefit, it would be fine.