Let me make this as clear as humanly possible to you, since you keep repeating the same arguments. Here is a link to the original trial court opinion:
Opinion. In it, Judge Tharp agrees with every one of your arguments - Backpage is knowingly engaged in illegal activity by allowing prostitution ads, Backpage has no rights to credit card processing and thus has no remedy, so no need for an injunction - on and on. Like most courts, once it involves sexual materials or content, they find against them as hard as possible.
By a 3-0 opinion, written by a Conservative Judge who almost got appointed to the Supreme Court (was considered for the position Alito got), the 7th Circuit rejected every one of the District Court's arguments - which are the exact same positions you keep regurgitating. Yes, the US Supreme Court might decide to hear an appeal, and yes, they could reverse it. But who is making conjecture now?
What you seem incapable of realizing is that, even if Visa and MC are not parties to this appeal, their lawyers are smart enough to recognize that the 7th Circuit just made clear that Backpage suffered harm having their processing removed - but it seems you are comfortable with public officials engaging in, as one Visa executive called it, blackmail. Most would say that would violate "public policy" and be one of those exceptions you keep mentioning. It seems pretty clear the 7th Circuit would be a good place for Backpage to sue Visa and MC, if necessary. But no one wants to do that, or spend the money, if they can first make an example of the public official who caused the problem in the first place.
So if Sheriff Dart orders CCBill and Epoch to hereby cease processing for all adult sites because children have been known to buy memberships and the process to ensure that only adults buy memberships is not 100% reliable, no matter what steps the billers take, you are okay with that? I mean after all, Backpage should be responsible for someone breaking the law, regardless of how many safeguards they employ, right? So why not CCBill and Epoch as well? Of course, Google and Bing deserve "safe harbor" protections because they are vanilla companies that just happen to allow adult sites to be listed on them....