Bleach hasn't really used cliched anime character archetypes in the past, in fact he seems to enjoy poking holes through them. The arc is young, and if she's a tsundere she's heavy on the dere.
No it's not that, it's like that "annoying bitch" is a stereotyped personality that has been showing up a lot more in recent anime. It's like a bratty, cutesy and angry over-the-top personality with some kind of psuedo-Western influence and it's silly. Another example would be in Gundam 00 (1st season if there were 2). Halfway through the anime the brown Gundams (i'm not up on Gundam lore) showed up and one of their three pilots was a young woman with the exact same kind of personality. It's like watching a 4 year-old flap around in a teenage body.
Nena Trinity, although I would agree follows the childish/whimsical brat female character archetype - she wasn't over-the-top angry so much as a thoroughly troubled sociopath. Her character was meant to be juxtaposed with her psychopathic and malevolent actions - It sort of expresses the dissonance between the seemingly pure but deeply corrupt nature of the world. Less symbolically, it shows - without directly stating so - the mistreatment of the character in her personal history which is an overarching theme of hidden atrocities in the falsely peaceful world. They tried the same thing with Stellar in Seed Destiny, and all the way back with Four Masamune and Elpeo Puru or Puru Two (though she/they technically were quite young) in Zeta and Double Zeta. You could say it's a common technique employed in these series where were lead to empathize with the fragility and purity of the enemy pilot which the protagonist is inevitably forced to fight, rather than simply employing wave after wave of expendable villains.
I was more confused about the Nena Trinity-like character in the 00-Gundam movie, that felt much more like pandering.
