Did you meet Zimmerman?
If he couldn't have hair, then his dopplegangers would most certainly not. besides, if his dopplegangers did have hair, or even too much hair, the public at large would think that he had deep psychological problems starting with an inferiority complex.
I'm really surprised that by 2378 that there weren't update patches which forced the EMHs to take on Zimmermans new decrepid likeness... If the line hadn't been decommissioned already, that is.