Saying 'rest' in peace, or more often writing R.I.P after a deceased person's name, is primarily a way of showing respect to the dead person and the feelings of their relatives.
And that is the reason WT would not promote saying R.I.P. If it is a tool of the devil to remove ones hat or tip it to the ladies, and if it is a tool of the devil to stand up when a woman enters the room, then "evidently" it must be a tool of the devil promoting self-worship to show any respect for a dead person or their relatives by saying-thinking-or writing R.I.P.
Now didn't I sound like a "good" little Dubbie?