I think these are only really helpful after you interview and not in getting interviews.
I beg to differ. I sent out LOIs to all my schools as soon as I was complete, asking for interviews, and it turned out to be surprisingly effective. (I got 8 interviews, and was accepted at 2 places and waitlisted at 4 others.) In several cases, I have direct proof that the emails worked, because I got replies from admissions directors saying, "Hi, I got your email and we're going to be inviting you for an interview."
I felt I needed to do this because my numbers didn't look phenomenal (in particular, I had an unbalanced MCAT score), but I thought I had compelling explanations for that, as well as a strong application in every other respect. I had one school put me on hold very early in the season, and realized that others might do the same thing unless I made a "pre-emptive strike," as the OP put it. I think I was right.
OP, don't let anyone here tell you there is a "rule book" for when to send LOIs, because they have no idea what they're talking about. If you want to send a letter, send it, and good luck to you. You do have to realize that most of the time it won't make much of a difference in your chances, but some of the time it might--and there's no way it could ever hurt you. (Who is ever going to resent you for telling them how much you love their school?) Just make sure the letter is well-written, succinct (a page or less), and clearly states why you like the school and what you feel you could contribute there.
BTW, there's also no law saying that you can't send multiple LOIs to the same school. My first round of LOIs got me about 3 interviews, but I followed up with a couple of additional rounds (these were based on "updates," not just saying the exact same thing as the first one). Each round brought me at least a couple of additional interviews. And for any school I interviewed at, I followed with an LOI after the interview.
If you're an applicant with strong numbers and a typical story, but you're just nervous, it might not be necessary to do all this. But if you have a strong feeling that you might get passed over without making an additional case for yourself through LOIs, then go for it.
Good luck.