Right, but the SCOTUS isn't the legislature - this is the judges appointing an advocate for one side, not an interested party (congress) choosing an advocate to represent their side. To treat these cases an analogous implies SCOTUS is a party of interest against the appealent.

Yeah, I think your last sentence captures what's so wrong about this. It just shows complete contempt for the principle of impartiality. Doing an end run around their AG should be Oklahoma's problem.