I've had a few basses where they have been in the case, and I have tried them - particularly on the Miller jazz I had, but ultimately they just get in the way for me.
I like to change where I pluck the strings a lot so any cover over the pickup just gets in the way. The bridge cover is always a no as some tunes really need a plectrum and a bit of bridge muting.
I like the look on the Miller jazz but it's not usable for me.