I think I can guess (Freakonomics-style) what the point of the exam is, instead of an out-and-out lottery. It's all about the perceived value of the school, isn't it...
If you have to Take The Exam to go to school X (even if the result is irrelevant), but school Y allocates by lottery, then school X must be better, right? So X gets better quality applicants (even after enforcing the banding) and its results go up. Everyone's a winner.
Except school Y.
And of course the kids who actually do the exam and get told, "you didn't get into school X, but don't worry, it's not your fault".
And the parents who have to transport the kids miles across town.
But apart from that...