The attraction is obvious. Instead of having to image ourselves as having powers which might destabilize our lives (à la Spider-Man), we simply become the hero we doodled on the back of a notebook. Anyone can do it, and you're allowed to ignore that decidedly un-super physique in the mirror. It's not just kids, it's adults too, but I stuck to minors in the list above because they best exemplify this idea. Because in addition to gaining powers above those of mortal ken, the very idea that it turns them into adults - or really, the IDEA of adults, since they'll have none of responsibilities beyond crime-fighting - increases their power in the world considerably. Captain Marvel can walk talk and get respect and admiration, he's strong, powerful and charismatic, but he'll never pay taxes, or get a job, or worry about his health.
And perhaps that's why modern writers have difficulty with the archetype. The Marvel Family has slid into corruption in all but the all-ages books they've appeared in, Dial H is about adults, and Ninjak has been divorced from that concept. Because if you apply your adult cynicism to the idea, there's no getting around the ickiness of a child in an adult's body. Basically: How do we address that being's sexuality? Answer: WE DON'T. It's a magical idea. Pure power fantasy. Trying to make it "realistic" or as a way for the child/teen to misbehave using that power is counter to the core of the archetype. It is the domain of alternate universe stories like Kingdom Come, and should not be applied to continuing characters lest they become distasteful or irritating.
What do you think? Are older readers unable to even enjoy this trope without looking at it cynically? Or since THIS older reader can manage just fine, is there an age window with which the archetype doesn't resonate?