There is no evidence Rav Aharon Kotler zt”l prohibited eruvin in Brooklyn. That he signed the 1962 Manhattan kol korei only proves that he prohibited a Manhattan eruv. It might be that the reason Rav Aharon signed on the 1962 kol korei was that he, like most rabbanim, accepted that Manhattan is classified as a reshus harabbim of shishim ribo ― as most rabbanim were under the impression that there was one street that had shishim ribo traversing it (Oznei Yehoshua, 1:18; Tirosh VaYitzhar, siman 73; Mahari Stief, siman 68, and V’yaan Yoseph, 1:195).
While the rabbanim of Manhattan relied on mefulash u’mechuvanim m’shaar l’shaar and mechitzos to allow an eruv, Rav Aharon maintained that nevertheless Manhattan would be classified as a reshus harabbim and an eruv would not be permissible (see Mishnas Rav Aharon, 6:2 for his reasoning). However, if the reason Rav Aharon prohibited the Manhattan eruv was that he accepted the Mishkenos Yaakov’s p’sak (O.C. 120-122) over the Bais Ephraim’s (O.C. 26) ― that shishim ribo is not a accepted fundament of a reshus harabbim ― almost all of the Achronim, including Rav Moshe Feinstein zt”l, would disagree since they maintained that shishim ribo is an accepted fundament of a reshus harabbim (the criterion of shishim ribo has been the accepted basis for eruvin for hundreds of years up until the present day, including eruvin in Eretz Yisroel and in many other large cities; see Part 2a: Why Brooklyn Is Not a Reshus HaRabbim).
It is important to note, that if Rav Aharon zt”l objected to the criterion of shishim ribo there would be no city, large or small, were we would have the ability to erect an eruv of tzuras hapesachim. This is since almost all city streets meet the criterion of 16 amos and Rav Aharon maintained that the criterion of mefulash u’mechuvanim is conditional of a walled city.