The point of the new regulation is to allow authorities who find your drone (like after a flyaway) to identify the owner without having to physically manipulate it and take off the battery. There has been an increased concern that drones could be rigged to explode when handled, so the FAA changed the rules to require the ID number on the outside.
Without your ID number on the outside, there is an possibility that responders will need to treat your found drone as potentially hazardous and call in the bomb squad, etc to verify it is safe. If this happens because you failed to place your ID on the outside, prepare to be billed for the additional expense at the very least.