Prophecy will indeed return in the Messianic age. Yoel Hanavi (chapter 3, verse 1) prophesies that in the future, there will be a return of prophecies, dreams, and visions.

Prophecy will indeed return in the Messianic Era. Yoel Hanavi (chapter 3, verse 1) prophesies that in the future, there will be a return of prophecies, dreams, and visions.

To answer the part of your question about Rav Kook: And although the inclination for worship of physical idols was taken away, there still exists other idolatries nowadays. According to Masechet Avodah Zarah 14b, Avraham Avinu composed tractate Avodah Zarah, and that our editions of the masechet only contain 5 out of the 400 chapters originally composed. For example, anger is a form of idolatry, yet it was not taken away. Masechet Shabbat 105b states "One who tears his clothes, breaks his utensils, and scatters his money in his rage should be in your eyes as one who commits idolatry." We do not know the extant of all the types of idolatry that were not taken away, so we also cannot know the extant of all the types of prophecy that we not taken away either. Anger (a form of idolatry) was not taken away, so too it would logically follow (as I understand) that certain types of prophecy were also not taken away. This goes in accordance with ShmuelBrin's answer that a "prophet" can exist in exile, because certain types of prophecy exist here. The evil inclination is not a bad thing as long as we are able to control its force and harness its energy for the sake of good.