I realize now, there are a couple different definitions to the word "preferred."
(1) to put before something or someone else in one's liking, opinion, etc.; like better
(2) to give preference or priority to
You are absolutely right by definition 2, there is no reason to prioritize one reference frame over another. Namely because all reference frames are equally valid.
However, I was thinking of the more "opinion" version of preferred (definition 2). As in, most people would prefer to watch a football game in the rest-frame of the football stadium, as opposed to the rest frame of some muon traveling past the stadium at near the speed of light.
Your statement above: " If you pick the muon's frame, you will just see a bunch of weird coordinates
that you will then have to reinterpret to determine what someone in the stadium actually sees." is confusing, though. That actually does sound like something out of "The Matrix." ;)
I don't know if you've seen this movie, but there are scenes in the movie, where mathematical symbols are more-or-less falling from the sky like rain, and there were parts of the movie where they really did "just see a bunch of weird coordinates."
I'm sure that's not what you meant, though.