A few additional thoughts. I have YU Semichah. I passed five tests in Halachah to get the Semichah and none included even one question on Mikvaos. It would have been a very good idea to require all Musmachim to learn Mikvaos as well as Ksamim which I did learn even though they were not part of the required curriculum.
There was one time when the Rav spoke for 25 minutes at a public meeting in which he took extreme exception to the derech of Dr. Belkin. I recorded it and typed it out. Unfortuantely, I lost it many years ago.
The Rav was very flexible. He tried to stay far away from the university politics and any other Machlokes that he could avoid. Dr. Belkin was a big Talmid Chochom and could give a Shiur. But his funciton was that of University President and only held an honorary title of Rosh Yeshiva. The Rav gave his derech of learning to thousands. Unfortunately, the Rav found himself in many machlokos because of his YU position and some ideas that were attached to him by default.
I remember a Talmid going up to him and asking him if his wife should wear a Sheitel. He responded, “At all times.” When asked about the Rebbitzen, he shrugged his shoulders but did not answer. He held that a shul without a mechitzah had no kedusas beis knesses. He held that one should not etner it, yet he did hold that one may enter near or even in it to hear the shofar if there were no alternatives. Most of the other Gedolim held that one may not enter it even if one would otherwise not be able to hear the shofar. Many of his Talmidim took synagogues without Mechitzos. Therefore many assumed that he permitted it. I only know of a few whom he permitted to take these pulpits and he placed rather difficult requirements. One was that they draw no pay, directly or indirectly from those synagogues. Another was that they had to daven at home, before entering those synagogues. And the third was that there had to be an agreement up front to vote in six months to install a mechitzah and that if the vote was not for the mechitzah, then the rabbi had to leave. This is a far cry from what most think his opinion was.