There seems to me to be a few reasons that the Book of Nahum/fate of Nineveh is important to Jews for all time. I am not familiar with Mishna/Gemara/Tosafot/Geonic materials(..yet...) so there could be plenty of Rabbinic views on Nahum, but to me the main reason that Nahum and Nineveh's fate are important is because Judah and Israel were oppressed subserviant tribute-bringers to the Assyrians for the longest period of time--at least 230 years. King Jehu is shown bowing down and bringing tribute before Shalmanezzar III on his Black Obelisk from 840 BCE. Later on Menachem started paying tribute in II Melechim 15:19. They oppressed, then destroyed the Kingdom of Israel. According to Pritchard's ANET, Manassah brought tribute and helped get wood for the Assyrian kings' palace. This lasted all the way to 612 BCE, when Nineveh was destroyed. Nahum assures Jews that no matter how long the oppression is, WE WILL SURVIVE(Thanks, Jerry!) their mistreatment and live to see their complete and utter payback. Another reason Nahum is important is because he says at the beginning of Chapter 2 "Keep your feasts Judah, perform your vows" showing that even under oppression, we should continue to behave as Jews--unlike King Ahaz, who tried to behave more like the oppressor(II Melachim 16:10). As for Nahum's length, after 230 years of oppression, nowhere near all of it recorded in Melechim, 3 chapters detailing Assyria's misery seems quite fair to me.