Did others notice how the media and liberal self-declared historians fawn over Democrat presidents and give many of them a loving nickname/acronym such as FDR, JFK and LBJ? (It isn’t anything recent.)
Or perhaps the initials were used to avoid confusion with Teddy Roosevelt, Robert Kennedy, Andrew Johnson (ok, not exactly a contemporary, but they were trying to be consistent). when it came to the Bushes, W sufficed.
According to your theory we would have had BHO and WJC, which we do not.