I am polite because I model the behavior that I would like the LLM to exhibit. I expect that, for the most part, alignment training (if nothing else) would cause it to not make very much if any difference, but it's a reasonable context cue, and I never know when or if it might matter.

Also, although LLMs don't presently train themselves on the fly answer-by-answer, I unavoidably train myself on the fly question-by-question, and I hardly want to de-train any habitual politeness I might possess.