Many do not. Those that do, will only do a face tattoo on someone who is already excessively inked. (Full sleeves, neck, hands, etc.)
I would NEVER tattoo my face, head, neck, or hands, but everywhere else is fair game. Over a 28 year span, I have underwent 37
tattoo sessions and currently have 2 scheduled, so obviously I am pro-ink, but even I cringe when I see face tattoos.