Dan Burke speculated, tongue in cheek, on the purpose of the church’s policies against facial hair stemming from a desire to protect members against archetypal authority figures, but the most likely reason for the policy is fashion cycles: the church’s historical acceptance of facial hair perfectly tracks the American fashion trend.
Facial hair was popular for American elite society only between the second half of the 19th century and the early 20th century. The clean-shaven look was popular at the time of America’s founding — none of the founders wore facial hair — and continued until around 1850. Until Abraham Lincoln in 1860, no major candidate for president had facial hair. Of the eight presidents who served between Lincoln and Wilson, only two were clean shaven. The last major candidate for president who had facial hair was Thomas Dewey, in 1948. This same fashion cycle is evident from Supreme Court justices, too: beards reined from 1860 to 1940.
Looking at the presidents of the church, they reflect this same fashion cycle. Joseph Smith didn’t wear facial hair, and Brigham Young didn’t either until about 1860. Every prophet kept facial hair through George Albert Smith. No prophet has worn facial hair since the mustached Dewey narrowly lost to clean-shaven Truman.
If you want advance notice of the church’s policy regarding beards, look to the major political figures. They are the bellwethers of the American fashion consciousness the church adheres to.