Just my two cents, but I can't help feeling that letters of interest mostly come across as brazen groveling. I just don't understand why a school (unless it's not particularly competitive) would have any interest in privileging one applicant over an other because they wrote a desperate sounding pledge of allegiance.
Adcom members are smart people- I imagine most of them see LOIs as a kind of sycophantism. I know we all have the urge to exert some control over this inherently unmanageable period of waiting, I just don't see letters like this reflecting particularly well on our case. We did after all demonstrate a strong desire to go to the schools we applied to by virtue of the essays we wrote and the interviews we gave and maybe even the thank you notes we wrote (or didn't). Even if adcom members don't view LOIs badly, I still can't see how they would actually make a difference.
When you compile a list of the criteria that most schools use to select applicants (GPA, MCAT, ECs, Essays, LORs, Life experience) how could a puny little letter make that much of a difference? It's been a while since I applied to college, but I never heard of such things as LOIs when I did and I did just fine. I've applied for a lot of jobs since college and other than writing a thank you note, it never struck me as anything but tacky and hyperactive to write additional letters detailing my enthusiasm for the job.
Of course I could be dead wrong. I have heard stories like the ones about Dean Frantz at Columbia putting a lot of weight on these letters. It's hard for me to believe though that he would care about these things until the waitlist season has started.