I was asked my opinion of the quote from Rav Aviner claiming that Rav Soloveitchik addressed the religious individual but not broader communal issues, unlike Rav Kook who provided a "complete method of understanding." It's a thought provoking quote, no? As for my opinion, first a few caveats: I am not a talmid of RYBS, so I am probably the wrong person to comment. My exposure to the Rav is limited to what has been printed. Secondly, I have not read enough of Rav Kook's torah to consider myself well informed about his views. Thirdly, my views on issues like this change all the time, so don't hold me to anything : ) This is just some off the cuff thinking aloud:
My first reaction was that addresses like "Kol Dodi Dofeik" do speak to the larger import of historical events and their impact the community. Yet, the more I thought about the quote, the more my mind kept coming back to the fact that the Rav's philosophical magnum opus is "Halakhic Man" -- not halakhic community. And it's not just "Halakhic Man", but in other essays the Rav uses typologies like "Ish Rosh Chodesh," the singular individual and his/her experience as a paradigm. Might the "Lonely Man of Faith" find comfort if he recognized a "community of faith?"
Isn't it odd that Rabbis Saul Berman and Avi Weiss have written essays in which they try to set out clear "gedarim" of what modern orthodoxy is, yet the Rav, from whom they drew their inspiration, never made an attempt to articulate a similar vision? How much clearer many of the issues under debate in the MO world would be had he done so! I think it's this lack of a larger all-incompasing statement which motivated Rav Aviner's comment. I am reminded of the Rav's hesped for his uncle, the Brisker Rav, in which he explains the B.R.'s approach to Zionism. The Rav explained that his uncle was not anti-Zionist -- he simply had no opinion. Eretz Yisrael is to be discussed in context of a sugya in Hil. Terumos, a Rambam about kedushas ha'aretz, but there is no "din" of nationalism and therefore it simply did not exist on his map of reality. For "Halakhic Man" there is no larger philosophical framework (e.g. a philosophy of modern orthodoxy) in which halacha exists -- to the contrary, halacha is the framework into which all else must fit or be discarded. Secular studies, Zionism, etc. stand out as appendages stuck onto Halakhic Man, but not part of his essence, his core. But for many of us these are core issues, and we struggle integrating these ideas into the larger whole.
I am only an amateur dabbler in Rav Kook's writings, but from what I have read he stands at the opposite extreme -- his writings flow in a stream-of-consciousness type way, speaking in universal ideals, philosophical broad strokes, and vision. I have never found in Rav Kook the precise gedaim which I so enjoy in Brisker lomdus and the Rav's typologies. As opposed to the Brisker tendency to split what appears to be one into tzvey dinim, Rav Kook takes the alma d'piruda and shows how on a higher level kodesh and chol, chiloni and dati, it all comes from one holy source and all is united. There are no appendages -- everything ultimately is one, oraysa, Kudsha Brich Hu, Am Yisrael, Eretz Yisrael. I think talmidei talmidim like Rav Aviner and other dati-leumi Roshei Yeshiva share a common perspective to a larger degree than the many talmidim of the Rav do precisely because Rav Kook articulated a more powerful complete vision, a vision that exceeds the confines of 4 amos of halacha and took in the universe as a whole.
It tool me two days to figure out how to put these thoughts into words and I don't think I did such a good job of capturing what I wanted to say, but this is only a blog and I feel free to take the liberty of playing around without crafting a polished essay. This is a topic worth spending more time on and revisiting at a later date.