There is a difference between Fantasy-The-Genre and Fantasy-As-Wish-Fulfillment. The former is it's own genre and big enough to have its own subgenres. The later is not a genre but a trope used by the author for their own sake or to appeal to a certain kind of reader. It is a unfortunate coincidence that a synonymy for "supernatural" is also the word for anything that one wishes to happen, supernatural, mundane or otherwise.
I strongly object to those that call fantasy novels for Audience X something that Audience X fantasize about. This is due to the kinds of characters and plots they create.
Its purpose is not to tell a story but give someone something they want while simultaneously reminding them that they don't have whatever that is. It's empty and hollow because it contains nothing but a spotlight. It's often poorly written, possess shallow side characters and a vague world because the page-space is used to show how great the protagonist is. It feels like junk food. I don't want genuine fantasy associated with these things.
A kid having magic powers can be wishful fulfillment and fantasy at the same time, but it is always the later and not necessarily the former. Dark Fantasy, for instance, would be about a magically powerful kid in a dark setting that no one would want to go to. That's for getting scared. Wish fulfillment is like this one book whose review I read. (It will remain nameless because I don't want to name it in a such a context). It was about this superpowered kid whose parents allowed him to drive a car, by himself, with only a learner's permit. The first part of that sentence is Fantasy the genre and the second part is a fantasy that a teenager might have. If the superpower were mind control it would make sense but it's not, so it feels like it was put there because a potential reader for this book would want to do such a thing.
This sort of Wish Fulfillment fantasy can be seen among the "Three Varieties Of Protagonists ", for all of them can be used in pseudo wish granting. The Champion is everything the reader wishes they were, The Loser is everything they're glad they're not (or someone that could hypothetically sympathize with them) and the Everyman is a self-deception so they can believe these things are happening to them personally instead of a story book character. Regardless of the kind of protagonist, everything is subordinate to this protagonist and how this protagonist can cater to the reader. The internet has given a name to such a character: Mary Sue.
In a nut shell, the Mary Sue is a overly idealized character that is often an Author Avatar. They were originally found in fanfiction where they outshined all the canon characters and since then they have expanded to original series. They can be both "mundane" with their perfection (beautiful, rich, skilled at everything school/work has to offer etc) but also supernaturally (god-like power with many possible uses). Both of these can be called "fantasies" but more accurately they are both Wish Fulfillment with the later adding a supernatural element. There's a plot trope that truly combines them both.
It's called the Vampire Werewolf Love Triangle . Here the protagonist can have a "special and exciting life" in addition to being fought over romantically. There's a certain infamous book series built around this trope and whose author has admitted to making the protagonist as featureless as possible so girls could be better slot themselves into her place. Therefore, a genuine plot and character development do not occur.
That's my problem with all of the above.