Physicists: Is the Star Function More Like Gleason's Theorem?

I think the mix and match approach kind of muddies the waters a bit. You could just say okay let's talk about what measurements ought to be so that this is carving up the theory in different ways or looking at the theory from different perspectives. I'm not completely sure that one is more natural than the others. The star function seems just to be a combination operation of some kind to me. It still feels mathematical but that way not really like a computational mathematics instead of postulate mathematics does that make sense?