Same way, why can't any brave gothamite shoot Joker? Joker's not immune to bullets, doesn't have super speed and insanity doesn't make you have any kind of super-powers, so any loose bullet could solve that problem. Why not?
If your take of a villiain is to make him so realistic it's perfectly plausible any girl can beat him, then why bothering in making him an important villiain in the first place. I can get Rachel beating those train's thugs, but that's it. If you're taking a popular villiain from the comics, make him face Batman, that was the idea in having him as a popular comic villiain to start with. We have a long development for Crane to become the Scarecrow and when he finally is, when he becomes as dangerous as he could be... we find out any person with a tazer can beat him. Flop.
Rachel could have easily used his tazer against Ra's when she had him close to her (and he wasn't aware she was close because he thought she was under the gas' effects which wasn't true). It could have been perfectly realistic and plausible and yet a lame way to end the conflict since it rules Batman out of the equation.
I still fail to see how Rachel "defeating" Scarecrow somehow makes Batman useless or obsolete. You're speaking as if she did something that Batman was incapable of doing, which was clearly not the case. I would be able to see your argument (and agree with it) had Rachel defeated Crane immediately following Batman's flaming dive out the window. It would've showed that, where Batman failed, Rachel succeeded. And that would've been lame.
But Batman faced Crane again, and DEFEATED him, incredibly quickly, at that. He cut off that punk's attack from out the corner of his eye, doused him with his own medicine, scared the living crap out of him, and bashed his head against a pole, knocking him out cold. He was then hauled off to Arkham where he would've remained had it not been for Ra's goons. It was only during Crane's third attack, during which Batman was not present, that a prepared and clearheaded Rachel was able to surprise Crane with the taser. And since his defeat at Rachel's hand is decidedly even
less final than his first defeat by Batman, as he was simply sent off into the night instead of sent to Arkham, we'll likely be seeing Batman in
TDK, doing what he does best - defeating Crane a second time.
And besides, if you really want to get out of personal preferences and into narrative and dramatic technicalities, Scarecrow was not the primary villain, anyway. That role goes to Ra's, who was dispatched by...who? That's right, Batman.
The secondary villain is traditionally fair game for the sidekick or secondary hero (in this case, Rachel) to take out, without lessening the importance of the main hero. Did
BR shortchange Batman by allowing Selina to defeat Max? Or what about
Die Hard? McClane beat Gruber, but it was Sgt Powell who ultimately took out Karl (who apparently McClane was unable to defeat by himself). Does that make McClane less of a hero?