have you ever responded to a HR rejection email?

I got a rejection email directly from the HR person I had a phone screen with, and I'm wondering if I should respond. I have very applicable skills and I know I'd be good at doing the job but what got me dinged were these really stupid questions after taking the interview on a day's notice. I'm being honest about the questions being stupid/irrelevant that showed nothing about my ability to do the job. Should I bother emailing HR saying something like I'm disappointed to hear that but I am the best candidate for this job because of X and Y, and I'd be interested in being reconsidered if none of the candidates work out? Of course in a more formal manner.

I know most would say to move on, but I'm sort of in a desperate period of my life.