If you do send a rejection letter, at least make sure it has proper grammar and spelling, and please send it within, idk, 6 months?
I have gotten some amazing rejection letters, but only after an interview. These are well-thought out, globally applicable to all rejections, and directly show why I wasn't a good fit. In sum, they were impossible to argue with. I've only received a handful of these, but they were worth keeping around for inspiration.