A screw to fill the servo mounting hole would be over 3/16 of an inch thick and impractical. The servo screw holes are drilled into the mounting plate so that the screw flanges (or washer, if I'm using one) snug up to the servo case and the shaft of the screw is snug to the inner surface of the hole. This is so that if, for some reason, the screws loosen the slop will be minimal. It is not the screw filling the mounting hole in the case that makes the servo mounting solid, it is the pressure that the four mounting screws apply to the servo mounting ear that secure it to the mounting plate.

Do a test, mount servos up both ways and work them back and forth to simulate usage forces and see what you think. Go with the method that makes you more comfortable.