I've had some thoughts about why, within the HPMOR world, it makes sense for Voldemort to choose to occupy a dementor-kissed body. I don't know the details about how the magic works or the solution to the HPMOR!mind-body problem, but it seems like it would be easier to take over a vacated body than to try to share the space with the original soul. It seems like a cleaner process, with no ambiguity about who's in control within the body. Second, based on Voldemort's personality (assuming that's what we're seeing from Quirrell) I think he'd prefer to be alone rather than having a roommate as he does in canon. Third, removing the original Quirrell also removes the need to rely on him to keep the secret and not give himselves away out of stupidity, lack of self-control, poor acting skills, or outright betrayal. Finally, other people might be able to tell when a body contains two souls - if the Sorting Hat can do it, why not the Hogwarts security system?
[Update: and now there's a fifth discussion thread, which you should probably use in preference to this one. Later update: and a sixth -- in the discussion section, which is where these threads are living for now on. Also: tag for HP threads in the main section, and tag for HP threads in the discussion section.]
The third discussion thread is above 500 comments now, just like the others, so it's time for a new one. Predecessors: one, two, three. For anyone who's been on Mars and doesn't know what this is about: it's Eliezer's remarkable Harry Potter fanfic.
Spoiler warning and helpful suggestion (copied from those in the earlier threads):
Spoiler Warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.