Really? I find the girls in Avatar to be a prime example of number 2, myself. Katara, at the start, is shown to have little control over her bending, yet after a few days training with Pakku (and self-taught training when she's not with Pakku) she goes to a master-level waterbender who can beat anyone she goes up against, including Azula, another "I'm super good because I just am" girl character (in the season 2 finale we see her countering everything Azula throws at her and it isn't until Aang fights Azula that they start to lose). This worsens in the third season when she gains control over Bloodbending, a technique only an old woman with years of forced practice in prison could use in about a few hours of training.
Even Toph was shown out-bending even the most experienced people with ease. She also created/perfected metalbending, which even the likes of Bumi and other Earthbenders couldn't do. Toph's "disability" also showcases more Number 2. The fact that her blindness actually makes her see better than anone else in the world, as well as giving her abilities like her lie-detector and earth-sense abilities just reek of number 2.
One could argue every Avatar character falls into this hole (it seems like kids can become godly benders which can defeat adults easilly unless they're a "wise-old mentor" figure like Iroh or Pakku). Even Sokka is shown taking down soldiers left and right and even powerful people like Combustion Man, but that doesn't make it any less valid I think.
Balance really is the key. Going back to Will, for example. She's not boycrazy, but at the same time she's not the "tough girl who doesn't need any man in her life" that you can find in a lot of Hollywood movies and stuff. She likes a boy. One boy, not all of them she sees. She also actively pursues him by striking up conversations, going on dates, and actually instigating a relationship with him, and they start going out by the end of the first season, where most shows will just have them crushing on a person for the entire series, then have them hook up suddenly in the finale without much development towards it (Danny Phantom does this, and Avatar as well, though Aang is the one with the crush) We also get to see her grow and become more confident and a better leader, but still make plenty of mistakes and underestimate her enemy, which causes her team to lose most of the battles they fight, just because they're simply outmatched by their foe. Despite all the losses, though, we definately see her grow from it and never becomes an overpowered character who can trounce all over the villains. In fact, the main baddie isn't even taken down by her, she has to use her wits to have someone else take them down... but even that leads to yet another mistake.