A problem with this is that there are several examples of chazakos in the Gemara that Poskim rule to no longer be true. For example, there is a chazakah that a woman would not be so bold as to declare in the presence of her husband that he had divorced her unless it was in fact true. But the Rema (Even HaEzer 17:2, citing others) states that nowadays, when chutzpah and pritzus are prevalent, that chazakah is no longer fully valid. Apparently, they did not consider this chazakah to be a permanent ontological principle rooted in the very depths of the human personality which is as changeless as the heavens above.
It may be possible to draw a distinction between these cases. Rav Soloveitchik explicitly stated that the reason why the chazakah regarding a woman wanting any kind of marriage is a "permanent ontological principle rooted in the very depth of the human personality" is that the Gemara bases it on a verse in the Torah - the curse of Eve in which it is stated that her desire shall be for her husband. Thus, perhaps only where a chazakah is based on a Scriptural exegesis is it timeless and sacrosanct.
The problem with this resolution is that the rest of Rav Soloveitchik's speech doesn't mention anything about such a qualification. It certainly gives the implication that all of Chazal's chazakos, and indeed all their statements, are timeless and sacrosanct. The Rav writes about how historicizing any of the rulings of any of the baalei mesorah over the ages is unacceptable. So how are we to reconcile this with the fact that historically, Poskim did not view Chazal's chazakos in that way? Furthermore, many people (and especially historians) find it very difficult to accept that Chazal were not in any way ever influenced by the world in which they lived - yet the Rav described this view as heresy!
Even more strangely, the Rav seems to describe such as an attitude as falling under the Rambam's rubric of makchish maggideha - denying the authority of the bearers of Torah. Yet Rambam surely used this term in a very limited sense - to those such as Tzaddok and Baytus who denied the very fundamental nature of the Oral Torah. As Dr. Marc Shapiro has documented at length, Rambam himself modified numerous concepts in the Gemara that were originally superstitious in nature. And authorities from Ramban to Vilna Gaon to Rav Hirsch felt no compunction in pointing out in turn that Rambam was influenced by the Greco-Muslim philosophical world in which he lived!
Perhaps the answer is as follows. Rav Soloveitchik's main concern was that, as he explicitly stated in that speech, once one starts to tamper with Talmudic halachah, this will end up destroying Judaism:
"Entertaining the possibility of revising Talmudic halachah at a rabbinical conference is as nonsensical as discussing the adoption of communism at the Republican National Convention. It is a conversation about suicide for the Orthodox community, the self-destruction of halachic Judaism."
This statement is, of course, entirely correct, and it perhaps provides a better reason for understanding the difference between the chazakah discussed by Rav Soloveitchik and that discussed by Rema. In Rema's day, there was no concern about the wholesale reform of halachah. But in the twentieth century, this was a very legitimate concern.
One way to counter the problem of reform is along the lines of Rav Moshe Shmuel Glasner - to note that the Gemara has been canonized, either formally or de facto. As for the counter-argument that Rema's ruling shows that it was not canonized so firmly, one could respond that since that time, and in light of wholesale reform, it has been canonized more absolutely. But Rav Soloveitchik instead took a different approach, claiming that chazakos were always timeless ontological principles. Did he really believe this to be the case about all chazakos, even that described by Rema? I don't know.
(Over a decade ago, an extremely charedi Rosh Yeshivah mentioned to me, as an example of nishtaneh hateva, that in his view, the chazakah that a women would prefer any kind of marriage to being single was no longer true, in light of the increased financial and social independence of women. He was masiach lefi tumo; he had absolutely no idea that this was something that Rav Soloveitchik had described as heretical. Had he been aware of this, or of the situation with Rabbi Rackman that caused it, he would certainly have said the same as Rav Soloveitchik. It's all about context. The view that Chazal were mistaken about science can be tolerated in a footnote in the Artscroll Shas, or in a restrained, apologetic manner in Yehudah Levi's books - but not overtly, as in my books.)
I once discussed this with a rabbi and historian who was a disciple of Rav Soloveitchik. He told me that Rav Soloveitchik's vehement opposition to the idea that some of Chazal's views and rulings were the result of their historical circumstances was a result of Rav Soloveitchik's historical circumstances!