Using the middle initial imparts extra formality, and in some corners, respect and importance to the individual's name.
Trivia - In my church (LDS/Mormon), it is traditionally ingrained in the Mormon culture to say the full name of every "apostle" or "prophet".
The odd tradition likely started as a practical way to differentiate Joseph F. Smith (a president/prophet in the early 20th century) from the original founder Joseph Smith (died in 1844). My guess is that it sounded unique so it became the Mormon version of, "So and So THE THIRD" - only without the disdain and with some religious reverence/awe sprinkled on top.
So now we have leaders with names (in any church PR) like David O. McKay, Harold B. Lee, Spencer W. Kimball, Howard W. Hunter, Gordon B. Hinckley, Thomas S. Monson, Russell M. Nelson... and so on. Joseph Fielding Smith was the only exception (since "F" was already taken).