Both the Supreme Court and the appeals court went into quite a bit of detail as to the necessity of achieving what the government wanted, because it was relevant to justifying the impact on speech with regards to the first amendment.

Only the appeals court (and presumably the district court below them) heard arguments about it being a bill of attainder. The supreme court chose not to. With regards to being a bill of attainder the appeals court appears to be of the opinion that it is enough that it isn't a traditional punishment, and that the justification for it was something other than punishment, without analyzing whether the government had a legitimate interest in achieving their non-punishment purpose. Of course they had already found that they did have a legitimate interest because of the first amendment analysis, but I don't believe their opinion with regards to it not being a bill of attainder relied on that.