It also doesn't show up for the female beast races. I'm playing as a female Khajiit and the mask won't show up

Because you have a muzzle, if the mask was on your face would clip through.
Well beards work just find on all the heavy armor helmets. They can easily fix this issue
The Nightingale and Shrouded cowl seems to cover the entire face and the lower jaw, rather than just the front of the mouth.
The nightingale hood works without beards. There's no reason wearing a masked cowl could disable the beard model for the duration of the helmet being worn.
As has been explained again and again and again, Fullhelms such as Dwarven, Daedric, Steel Plate and Nightingale hood's completely replace the head, not one facial feature remains visible. Its why beast races don't clip through with their muzzile or ears.
The Nightingale armour mangages to remove the players hand and replace them with darker ones. They could just show the eyes. It can't be that hard just showing the eyes if they are able to remove the head in helmets. If they knew it wouldn't work why did they leave it in?
The armor has gloves which cover your hands, the "visible fingers" are actually part of the gloves. Its why you have the dark skin on a pale Nord. Removing the entire head is easy, the helmet simply replaces the head. Its partially covering the head thats so complicated. They left it in because the mask still works for human females. The fact remains that PC modders have failed to solve the beard clipping issue when they fix the masked cowl.