Michael's power base in 3 is never credibly explained. On the one hand, Zasa commands what used to be the Corleone street operations in NYC (the "olive oil business"), as he told Connie and Vincent at his party. He "sold all his shares in the casinos," as Abbandando explained to the reporters at his party. And, after the casino shooting, he mutters, "Just when I thought I was out, they pull me back in."

On the other hand, Michael is, as you point out, "the Supreme Court" of the Mafia; has enough power to prevent Zasa from rising in the Commission; presides over a Commission meeting in AC, and distributes profits from some unknown source. He couldn't have maintained that much clout among top organized crime figures without having his own organized crime power base.

The main weakness of GF III is the script, and this is an example of that weakness.