They were there for looks as well. To cover up the pick up and bridge. To give it a clean finished look, not having the "working parts" exposed.Not just for looks folks, they were designed to serve a purpose. These days, I’d say most bassists have them onboard for aesthetic reasons or to be true to the original design. I have them onboard some of my P basses for their original purpose.
The bridge cover holds the mute and the pickup cover is a palm rest!
Leo originally designed the P to be plucked with the thumb using the tugbar to anchor the fingers and the pickup cover gives a spot to rest the palm to prevent mashing the stings into the pickup. Bassists that had a more traditional plucking style using index and middle fingers also used it as a palm rest. Jamerson is a good example, using a floating thumb, index finger, and resting palm on pick up cover. That’s how I use it too. Nowhere near as good as JJ did, but I use it for the same purpose. My bridge covers are stuffed with foam. Boom, boom, boom.
On my other Ps that have rounds on them, I strip the covers and go for max sustain, usually with a pick. No need for mute or palm rest.
Hope this helps clarify some stuff.
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