The cover protects the coil wires from damage. If the covers are made out of metal, they also add some effective shielding to keep out noise. So removing them comes at some cost.

The wax is there to keep the coil wires and bobbins from moving, which helps to prevent uncontrolled feedback, and also keeps dust from wearing through the varnish insulation and shorting out some of the turns. So removing the wax comes at a cost.

Without the covers in place, the wax will quickly get coated in dust. Open coil pickups usually have cloth ribbon wrapped around the coils to cover the wax, but that was probably not installed on factory-covered pickups.

There was probably some wax between the top face of the coil and the underside of the cover to prevent any rattling or buzzing. You can gently scrape this off with something fairly soft, like a wooden toothpick. Using a knife, or a metal scraper, will scratch the face of the plastic bobbin, looking ass. And you must be very careful to avoid damaging the coil wires.

All in all, I'd recommend leaving your pickups covered. My go-to guitar has covered pickups. One pickup had a factory cover; I covered the other one so they looked matched. 20 years with no troubles at all. And they sound great!