Solid analysis as usual. Also as usual, I'm probably a bit more forgiving of inconsistencies and changes than you are - but I do agree with your basic conclusion that they made her character weaker, not stronger, despite the rhetoric from some quarters about how the books display a flawed, or even misogynist, take on women and how the series would do so much better.

Of course they could never have introduced her precisely the way the books did, but a better script, with probably a few more episodes and definitely less stupid invented filler, might have given us a bit more time in Emond's Field to get to know the characters prior to the Trolloc attack, like for instance with the first episode ending with Narg attacking Tam and Rand, then the bigger fight in town moved to episode two. The painful idiocy of Nynaeve's Trolloc abduction and subsequent miraculous escape obviously should've been tossed straight into the trashcan, and her interactions with Moiraine in episode one and with Lan in episode three should've been done better. All that might still not have been as good as the books, but it would've been good enough.