In the biography on R. Moshe (printed at the beginning of chelek 8 pg. 23) it tells that when he came to the U.S. he was offered a position in both Torah V'da'as and YU. He rejected both because "he is not interested in working for a yeshiva that is run by ba'alei batim".
Perhaps his concern was as the SM'A writes (C.M. 3:13) regarding a dayan who is going to sit on a beis din with ba'alei batim:
ואם תשמע לעצתי לא תשב אצל הקהל בשום דין דידעת שפסקי הבעלי בתים ופסקי הלומדים הם שני הפכים
This yesod is also expressed by the Maharsha on today's daf. The gemara implies that R' Avahu forfeited a public position because he didn't need the money and convinced them to take R' Aba d'min ako who needed the money. From this the Maharsha points out that in those days people would run from public position unless they had no choice, but nowadays it is the opposite, the more money you have the more you use it to influence to buy yourself the honor of public position. He then points to R. Yehoshua ben gamla who restored Torah to Klal yisroel by setting up a yeshiva system, and later bought into the position of kohen gadol and became a rasha [i seem to recall tosafos saying that it must have been a different person]. The maharsha then explains what he considers to be the root of the problem:
שהבעלי בתים הם הם הממנין ומבררים להם ראש כפי רצונם לפי הנאת כל אחד מהם וביותר בממון, אבל מן הראוי שהלומדים והרבנים בעצמם יבררו להם ראש וכו
Well, so much for democracy......
I once heard from a big talmid of R. Moshe that when the mishna 20a says that whoever teaches his daughter Torah it is like teaching her tiflus, and rashi 21b explains that it is a language of trickery and deceipt, should not really be applicable to women more than men. The reason why it says it by women is because they will generally not be shakuah completely in Torah since they have so many other responsibilities whereas men can be completely shakuah in torah. But, those who aren't completely shakuah in torah and aren't mevatel their da'as to what the torah is teaching, are the same as women where the Torah becomes a "tiflus".