I think sending multiple LOI is like the lowest unethical thing you could do. You aren't forging a transcript, You are not commiting a crime. You are basically telling every girls you see that you love them in hopes of getting that girl to go to prom with you. Is it scummy? Sure, but it is not really that bad considering how some schools will outright take your application money and give you a silent R. For the most part there is no one looking out for you but yourself.
Desperate times call for things like this. I think crafting a decent well thought LOI to the schools that matter most to you (ie not all the schools you are WLed in, an LOI to Yale probably does not do anything) is something an applicant should try. The worst thing that can happen is what you stated, the best thing that can happen is eventually getting off the WL. With those odds I think it is better to send 3-5 well crafted LOIs to high, mid and low tier schools just so you don't ruin your chances to all the schools you applied to in your reapplication.
At the end of the day premeds are fodder, nothing more. These schools do not care about you they are trying to meet THEIR needs and have the funds to do that. Most premeds DON'T. Sending a LOI is cheaper than reapplying.
Would I personally do it? I do not think I will. I am hoping I already have As by this time around and I would hate to beg to these institutions but I rather beg than go back to being a premed for two more years, being a lab slave, scribe slave or EMT slave.
Yes multiple LOI are scummy but you gotta do what you gotta do.