There is also a theory that the pickup and the cover create a magnetic pull between each other, thus making the bass louder when the covers are on.
I do not notice an audible difference without the covers but if you scope it, you'll see a difference.
I do own a 1961 Rickenbacker 4000, this bass has one original horseshoe pickup that has the metal cover, (not the plastic covers that Rickenbacker uses today) and there is a huge difference in the sound and pickup power when this cover is removed.
Treena