Maybe just to prime Harry with Azkaban, to drive a wedge between him and all magical authority that supports it, to prepare him to go Dark, and to be absolutely certain he'd act in a hurry if, say, Hermione was imprisoned there.
The other major effect of the Azkaban arc was to convince Dumbledore, and through him Madam Bones who commands the Aurors, that Voldemort has returned. While Dumbledore thinks Voldemort is around, he's less likely to suspect or investigate Quirrel as the cause of any new disasters; and he also prohibits Harry from leaving Hogwarts, which drives Harry to Quirrel for help if he must leave - such as, again, to help Hermione.
Besides, Quirrel may be right when he says he didn't think the Azkaban breakout was such a big risk (of discovery), he just didn't anticipate Harry interfering against orders and then stunning him due to the resonance.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: