I’ve got to agree with Bauer on this point:

One explanation provided to USA Today is that it will allow for a hearing at which the general public will be heard. But such a hearing has been held, and the Chair could have unilaterally arranged for another, as she did recently in convening a forum on the role of women in politics.

The answer to this may be no more than: it does not matter, because the Petition serves only to make a point. A sympathetic observer would call it a cri de coeur; one less sympathetic might see it as a PR maneuver. What might unite the two sides is merely their agreement, for entirely different reasons, that the Commission is not in good working order. The risk of the petition initiative is that rather than move the discussion to a better place (hard as that is), it sends a dreary message about the state of the agency.