I don't particularly think the official rules are terrible. I think they'd probably work fine for an all child game or for someone actually interested in playing a sidekick Shortround style character (though I can't really imagine why anyone would want to.)
They are obviously not intended to produce characters on the same power level as normal adults characters. That's pretty much the point of them.
As for actually allowing it, I'd consider it, based on what type of game I was running. The first question I'd have though, especially for a kid as young as an equivalent of an 8 year old human, which I believe was the proposal, would be: How do you intend to roleplay this character? As an actual 8 year, even if an incredibly smart and educated one, or as a miniature adult? If the later, why bother? And if the former, that's going to be incredibly disruptive, if everyone else isn't really on board with it. Third graders, even brilliant ones, are still working on basic social skills, emotional control, impulse control, delayed gratification and similar things.
There's a really fine line between not even bothering to roleplay a kid and just being a constant pain for the party.
A kid in the 12-13 range or even closer to normal starting age, I'd have a lot less trouble with. Especially if the kid came with a "had to grow up fast" backstory - which is a little hard, but not impossible, to match with a brilliant child with a very early education in magic.