Removing the covers gives you more bite, more string attack, Little more evenness with note decay, it is subtle yet noticeable, especially with mid gain and higher volumes,
Higher-quality less magnetic thinner pickup covers Can minimize the effects.
However if a metal can conduct electricity it creates a slight counter magnetic field as the string moves through the magnetic pole field.
Voltage current eddies are created. Certain frequencies and volumes are lost. But it's up to your ears, it is essentially a slightly different EQ with a cover installed.
I remove all my covers on my bridge pickup much better control of my string attack. Slightly less compressed. More responsive to your picking technique.
Here's an example of a technician putting the pickups on a frequency analyzer with and without covers.
Quote Looking at the frequency response graph.
You'll notice they all have "dips" ahead of the resonant peak, the green line, the unloaded Epiphone plot has a the biggest dip of them all, and that is a direct result of eddy currents reducing the voltage output as the frequency rises. Conductive metals in the presence of changing magnetic fields cause eddy currents which 'push back' on that same magnetic field which creates them, resulting in a net loss of magnetism and induced voltage. Faster changing magnetic fields, or higher frequencies, causing stronger eddy currents, so the voltage slopes downwards as frequency increases. The reason there is a peak after the "dip" is because then the resonant peak comes along and increases the voltage, in spite of the eddy losses. The gray line, the loaded gibson 57, shows a case where the increased voltage at the resonant peak is barely able to offset the voltage loss caused by eddy currents.