A few notes about R’ Soloveitchik, based on things I’ve read and heard from others:
First, his impact on Judaism in the US was tremendous. It was noted by AviraDeArah that many could have gone to learn by R’ Moshe or others. Yes, that’s true for some. And as was noted, many of his students built shuls whose members had functions with mixed dancing. But remember that the times back then were very different than they are now. Many of these people were not frum at all, or barely hanging on. They would not have sent their children to R’ Moshe, because he was too “extreme” for them. The Rav gave them a place where they felt comfortable, and he brought Torah Judaism to them, one step at a time. He definitely didn’t hold that mixed dancing was acceptable, but if someone was going to do it anyway, he believed that it was better to have them do it in a place which started with basics – keep Shabbos, eat kosher, follow the laws of taharas hamishpacha. Maybe the parents didn’t stop the dancing, but many of the children did. He shifted the observance level positively.
Regarding his Torah: as I’ve posted before, I learned in Darchei Torah. I personally know someone who asked the Rosh Yeshiva, R’ Altusky, about learning the seforim of The Rav. R’ Altusky told him, “Absolutely, they’re fantastic! I have them all at home, and you should definitely learn them!” The bochur asked why the yeshiva didn’t have them on the shelves in the Beis Medrash, and R’ Altusky replied that while his shiurim on Gemara were excellent, they still disagree on hashkafic differences. Some of the younger bochurim might not differentiate, and would think all his seforim should be learned. So they kept his seforim on Gemara in the library instead of in the beis medrash.
As for different students claiming different views on things (like egalitarian minyanim), R’ Schachter once said in an interview that things like this were a common occurrence. The Rav knew were the different communities were holding. In one place, a minyan where a woman carried the Torah around on her side of the mechitzah might be warranted, to get them to come to shul. In another area, he could have been adamantly opposed to it. It all depended on who was asking.
Lastly, about YU/RIETS in general: I once had a conversation with a well-known and respected Rav about it once. I also once spoke with R’ Bender about it.
First, the Rav I spoke with: he told me that he knows all the stories said about R’ Miller zt”l and R’ Gifter zt”l, and how they left RIETS because they felt it wasn’t frum enough. He knows the criticism that was said about it back in the early/mid 1900s. “And you know what? They were right! At the time, it had problems! But it changed. Do you want to know why? Because they started sending the boys to Eretz Yisrael to learn for a year or two after high school. And that made a world of difference. As soon as that started, RIETS and YU had a HUGE improvement! And the issues they had all those years ago are gone now!”
Rabbi Bender told me that he felt YU/RIETS gets a bad rap in the yeshivish world, and it’s not warranted. He told me, “Sure, we don’t send our guys there, because it’s a different hashkafah. But that doesn’t mean it’s a bad place! It’s excellent for most of the people who go there, and they have tremendous Talmidei Chachomim there!” He also pointed out that there were a few Darchei guys who he had encouraged to go to YU, because he felt it was the proper place for them.