I think Acidkid has it. They’d often like to have beards but department policy dictates no beards.
The department I work for specifically (written policy) allows beards. Which is lucky for a few of the female officers, because otherwise they would be in trouble!
But seriously. Our department is a rarity. Most don’t allow it, but that is changing a little (just a little) bit. More departments are allowing it.
I’ve found that departments locating in the northern part of the state allow beards more than those in the southern part.
The mustache thing is a tradition, but not really. I know just as many cops without facial hair as I know that have it. I only have facial hair because I loathe shaving. Taking a razor sharp blade to my face every day is not appealing to me. The mustache area is most sensitive on my puss, so I let it grow.