Communication is important, sure. But I don’t think it’s the most important skill for managers.
If communication was the key skill needed to be a great manager, it would imply that great managers could parachute in to run any old team, as long as they were able to communicate well.
But the best managers don’t just communicate their decisions; they need to exercise judgment and expertise to make good decisions in the first place. And making good decisions requires understanding your technology/product/team very well, which all go far beyond communication.