The safety of the child and the animal are the concerns. Larger species of calm reptiles are good for children 5 and up for short supervised handling sessions. Any smaller species should probably be left for kids 8 and up due to them being delicate animals that can die from injuries of a rough child. Even if you think your kid is gentle for their age, it only takes one mistake for that animal to be injured or dead.
Beardies are not the easiest or cheapest in terms of care/space needed/food, but a lot of people think just because the lizard is cheap that everything else will be cheap. They eat a tonne, poop a lot, smell pretty bad unless you clean all the time, and need a large enclosure despite their small size. They also need high heat of course. They can also mistake fingers for food, and an adult getting a bite from them can be pretty bloody, but a small child could need stitches/medical care. Adults that have experience with them know what to look for when they are potentially going to bite for any reason. Children don’t know and beardies move quickly, so even if you are watching them you may not be able to react quick enough.