I do not think you should accept LOI's. First of all, I agree with all of the above opinion that LOI's cannot be validated for authenticity. Secondly, as a applicant who currently has 4 rejection/no II, 1 waitlist position (at the bottom third, which for all intents and purposes a rejection), one additional wait list position (unknown position), I am exhausted, frustrated, and at times emotional. I began this application over 10 months ago and it has provided nothing. Of all people, I SHOULD be the one begging for acceptance, but I'm not. I believe that LOI's are just that - documents of begging. I think remaining stoic and patient throughout this process is the best way to display maturity. I like to think (whether or not anyone else agrees) that I have more self control than that. It's life. I have the rest of my life to work, and I'll get in at some point.
Furthermore, in the case of UCF, the admissions committee has already assigned me a score and will no longer accept updates. This was very clear on my interview day. A LOI will not change that score. By submitting one I'm either showing that I'm dense or arrogant.
If I ever found out that a program admitted another student over me just because of a pleading LOI instead of credentials, I'd be furious and never reapply there.
I think the best thing to do for anyone in this situation is to bow out gracefully and either apply to the program after AT LEAST A COUPLE more application cycles, or to sneak away and hope the program forgets about you and your inadequacies incase you want to return for residency, etc.