Petitions for Rehearing in the Supreme Court

A petition for rehearing is rarely granted by the Supreme Court. I can recall only one example in the last 2o years (Kennedy v. Louisiana). But I wonder why more litigants don't file one for PR reasons.

Consider a high-profile case in which there will be no further substantive proceedings. You lose in the Supreme Court. Why not file a rehearing petition pointing out why the Court's opinion is wrong or poorly reasoned? Unlike a brief, you can actually respond to the opinion rather than anticipating what the Justices may think. 

Maybe attorneys who are repeat players don't do this because they think they'll look like sore losers. Or maybe filing a rehearing petition just costs money that clients don't want to pay. But I'm surprised that you don't see more rehearing petitions at the Court.