Only where the dangerous situation can be made safe. Rock climbing is dangerous, but with a little training and equipment becomes safer than playing soccer. A chainsaw cannot be made properly safe, not for use by children, for the same reasons we have minimum ages for driving cars.
Maybe a smaller electric chainsaw? With far less power and therefore reduced bucking/etc? 100% get what you're saying. Chainsaws are risky use items for skilled adults.
It also isn't just the chainsaw but the implications of using one. Chainsaws are not used indoors. They are used on uneven terrain to cut things (trees/logs) that are irregular in shape/weight and subject to unseen internal forces. It's a setup for random movements an unanticipated results. Even for adults, felling a tree with a chainsaw is a very dangerous thing.