Well, that depends on the version. The chairperson really did act like the leader, and they didn't have that rotating thing in very long. Like pretty soon, the chairperson was elected by the team (ie how Jan, Monica, Vision, and Natalia were). So when Cap first showed up, they may have had the rotating thing in (haven't reread that of late), but he didn't rotate in for a while, and the first time he did, it was a big deal for him.

I think he's just a little overwhealmed too. I'm sure something will work out by the time they get the movie going.