Excellent points. My model above happens, but it’s not the only kind of argument. As usual, there’s a spectrum, and I was mostly just describing one extreme of it.
It’s also worth pointing out that logic or proper reasoning don’t weaken this kind of argument. They’re unnecessary, but if you’re well-put-together enough to use them without having to stop and think, they’ll make you seem all the more impressive. So, logic doesn’t ruin this kind of social grandstanding; it’s just not necessary
Yes, it is a sad truth that it is easier to explain a math equation to people if you’re good-looking, have a nice voice, competently play social games and other things that should be, but are not (and we must come to terms with that), irrelevant