Since you asked for anecdotes:
I had a pre-teen player join my table once (he was the son of one of the other players) and his character concept was just a mary-sue as you fear. He basically wanted to be Raistlin the Tiamat killer on session one.
So my challenge then was to find a way to mold expectations for this character concept so that he still basically got what he wanted without disrupting our normal game by having an overpowered PC fall into their midst.
I accomplished this by taking stock of his character bio and breaking it down to its essence. He described a brooding dragonborn with an exceptional talent for magic who carried an orb that allowed him "power over dragons" (I told you he stole this concept, right?), a wand that could shoot fireballs, and a ring that made him invisible.
I can feel the eye-rolling through the internets. Bear with me!
What he wanted in essence was:
- Powerful magic
- A connection to dragons
- Something fiery and flashy
- A way to be sneaky
The problem was the party was only 2nd and 3rd level. So here is what I did: I used examples from things he would recognize: "Hey, Luke Skywalker couldn't beat Darth Vader straight off Tatooine, right? He needed to learn, find a teacher, and eventually overcome the evil in himself before he could beat his dad. Our game is like that. You start off a bit weaker, and get stronger as you go."
I then gave him all the magic items he wanted but with caveats. The orb was indeed an orb that could control blue dragons, but it would only do minor things for him, like warn him if a dragon was nearby. he had a clue as to where to find hidden knowledge of this artifact and I turned that hook into a subplot of the group's adventure. Everyone had a great time with it over the long haul, not just him.
The wand of fireballs was legit, but only had one charge. Recharging it required a burnt offering to his Patron god, Bahamut, and cost him a price in gemstones. So he didn't whip it out every encounter, but rather saved it as a "holy heck we're gonna die" move. Even after he mastered the actual spell for himself, he kept it around as an ace in the hole and the party's rogue even used it once to save everyone when he went down.
The ring was a bit of a trick. Actual rings of invisibility are stupidly powerful, especially with clever players. For this, I simply had a frank discussion about it with him and instead it started as a minor magic item that only gave him advantage on stealth checks. Later as the orb-subplot advanced, we decided it would be cool if the ring and orb were linked, and it grew in power as his mastery of the orb grew. By level 10 it was totally a ring of invisibility with a few other minor perks and by that point the party was facing threats of a level where a single invisible player would not unbalance the encounter.
So in short, he got his wishes, but gently massaged into the framework of the existing group. If you can find similar flexibility with your young players, I think everyone will have an excellent time, even if their character are a bit stronger than normal at the beginning of the game.