Did Anu make his last personal visit to Earth in about 3000 BC where he mandated that because of massive infighting between Enlil and Enki, that rulership of Earth rotates among the three every 2160 years?

This is a correct interpretation of history. This was to give them all an opportunity to learn from the exercise and would serve to balance things, to keep peace at home, so to speak, for the Anunnaki brethren more so than to spare humans from the results of the discord. As in all done by Anunnaki, it was self-serving.