Pickup cover would probably detract and spoil the look.
Ashtray bridge cover can look good but has to be removed on every string change plus it robs you of the flexibility to do palm muting, if you're into that sort of thing. (obviously i do dabble in a bit of palm muting from time to time)
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You are correct. I have removed the Bridge and Pickup covers. So much easier to play....and palm mutes are a lot to give up.