“The crow of the rooster is fatal to it” is a rather silly rule. I wouldn't have used it if the Basilisk was a major character. Here, it provides a anticlimactic solution to one of the books' major conflicts, just like when Voldemort was eliminated after zir attack on Harry's family.

As I was designing Voldemort's Children, one of my principles was that the characters should be forced to make decisions without having a convenient Dark Lord to oppose or seemingly wise adult authority figure to look to for guidance. Compared to the other choices the characters make, the choice of how to dispose of the Basilisk is an easy choice. That's why I'm willing to cover it in a quick and even silly way.

As a side note, the statue in the Chamber of Secrets is supposed to be a full-body statue and not just the head. I would have drawn it that way, too, if I was going to use it on more than one page. I was even thinking of drawing it from a dramatic angle, as if the reader was looking upwards at it. But since it only appears briefly, I decided to use an image that some people would recognize from the films.