Militaries seem to have this weird hate/love with facial hair.
The "clean-cut" look common in the US military, prettyu sure was fairly recent - like 20th century. Going back to the US civil war - not having at least some facial hair (whether it was full beard, mustach or just mutton chops) was actually the exception.
In older times, the Romans and Egyptians were clean shaven, while the Greeks and barbarian tribes were not.
Even in WW2, German uboot crews allowed full beards - although that was probably for practicality more than anything. Not a whole lot of clean water to spare for shaving.
My theory is, some general / politician gets into power, decides what looks cool and feels that everyone should follow them. I think there's a fair degree of copying of whats considered the best army. E.g., the US copied alot from the Prussians / Germans in the late 19th century.