It seems that friction would make a difference in how the mouth, the lips in particular, engage the mouthpiece. So one player might prefer a smoother, another a rougher mouthpiece.
Alan, I’ve updated my post to define “mouthpiece” (it’s everything leading to the case, not just the part that touches the mouth) The question of friction, as I’ve heard it, usually concerns whether there is a loss of power due to differences in friction, so I’ve clarified that as well. Thanks for revealing that my post had some hidden assumptions
The issue you bring up is different, but I’m not sure exactly what how to frame it as a physics question. “Preference” is not a physics terms—it’s subjective and not relevant for this site. You are welcome to ask a question (as a new topic) if you can think of one for which an objective answer is possible