I find this absolutely incredible, that the workings of the court in a commercial case like this can be hidden from the press and the public. Disgusting that they would ask for this, and I sincerely hope that the court will reject that.
A company that gets bad PR as the result of a court case might be able to get the ruling overturned but that does not trump the right of the public to know what transpires in the courts. And no, then Apple could not - and should not be able to - sue for damages because they are themselves recognizing the power of the courts as arbiters in these matters.
Similarly: if the ruling is upheld Apple does not get to pay more because they - apparently improperly - asked for the previous ruling to be kept secret.
Courts should operate in a transparent manner whenever possible otherwise the trust in the legal system will erode and that trumps the commercial interests of any single company, even one as large as Apple.
In the court’s defence, these documents are rarely sealed forever. Usually they become public after the ruling has been made.
If an appeal is being made, and current decision being temporary suspended, then there's no reason for the original decision to be public. The courts decide on matters of law, so the publics view on the original decision is irrelevant, and up to the parties involved to convince the appeal judge their interpretation of the law is correct.
Once the matters been settled by the courts, it make sense to make everything public. But a no point during the process should or can public opinion influence the outcome.
More likely, it's merely evidence it's a legally sound thing to do. That doesn't mean it's particularly reasonable, simply that it's not technically trivial to reject out of hand. It could equally be a symptom of regulatory capture; it's not like the judge gets to just do whatever they feel is fair (at least not without professional consequences).