No, Moshe Rabbainu did not wear a hat. (Then again, I doubt he wore pants either.) And no, there is nothing intrinsically holy about a black hat. However, wearing a black hat shows that you identify yourself with the yeshiva community, who put Torah and Halacha above all else. (That is not to say everybody else does not, only that they do.) Not wearing a black hat normally shows that one does not identify with the yeshiva community. This association only devolved fairly recently, but it is true nonetheless.
“Personally I have an extra level of respect for those rabbeim i know who dont feel the need to put on a black hat when they themselves did not grow up with one because they live the ideal that chitzonius is sheker.”
I’m not quite sure I follow that… would you have extra respect for a Rav who dresses in a T-shirt and shorts because he “lives the ideal that chitzonius is sheker”?