The candidates and their campaigns could exert a lot of control over what those organizations did on their behalf. And if the organizations didn't cooperate, the candidates could denounce them and their efforts.

People seem to forget that the PACs and 527s arose in the first place as a way to get around the campaign finance laws. So what point is there in agreeing to take public money to finance their campaigns if they're going to be circumventing the law by relying on the PACs and 527s to do their dirty work for them? There is no point to it - it would be all just for show.