HaKatan,
1. It is not only incorrect that the Chafetz Chaim said “Kook schmook”, in fact, he walked out of the first Aguda convention when someone defamed Rav Kook, whom he held in very high esteem and, in fact, told to enter the rabbinate.It is true that some disagreed strongly with Rav Kook (and see Baba Meyzia 83b regarding what a rtalmid chacham can say and what an am ha’aretz can say)most esteemed him greatly. When Rav Shlomo Zalman Auerbach was a bachur he was a regular at Rav Kook’s seuda shelisheet and derasha and Rav Kook was his messader kiddushin. Rav Eliashiv called Rav Kook a gaon olam (and married a daughter of Rav Kook’s talmid chaver Rav Arye Levine).Rav Sonnenfeld joined him on his “teshuva tour” of the kibbutzim and moshavim and years later gave him a beracha that he should be Cohen Gadol.
2. As I have posted many times the vast majority of gedolim supported Zionism and certainly supported and continue to support the State.
3. When one of Rav Kook’s opponents saw him walking alone at night he reminded him that the Gemara says (Chullin 91a) that a talmid chacham should not do that because of the mezikin (Tosafot d”h mikan). Rav Kook replied tthat the mezikin of Yerushalayim did not consider him a talmid chacham.