It definitely happens most with Katy and Cody and mostly on BtB, but I don’t think it’s on purpose and I definitely disagree with OP about Robert not having great report with his female guests. Jaime Loftus and he have a great dynamic and in the episodes they did with just Katy a few months ago they had a much better rapport than when all three are present.

I think the issue is more that while they are all obviously close friends I think Cody is closer to both Katy and Robert than they are to each other. So since Robert is leading in BtB he’s starting the riffs which are often more in Cody’s wheelhouse than Katy’s. I don’t believe this was the case during worst year ever though because it was spearheaded by all three