Actually, the plural form of a driver's license should be driver's licenses because driver's is fixed in form here and is used as an adjective rather than a possessive. This is very common for products and utility items. For instance: McDonald's burgers, Wendy's salads, electrician's scissors, programmer's text editors, a voters' strike, children's beds, kids' TV et cetera. All these examples represent the same phenomenon where the apostrophe-s construction no longer indicates possession, but acts as a descriptive word the way a regular adjective does. So, if I say:
Do you know how to tie the angler's loop?
Well, it's quite obvious that this does not refer to a loop that's owned by a particular angler that only you and I know about, but rather it's describing the category of loops the loop under discussion belongs to.
It's a totally different story when we're dealing with the real possessive case. We're going to say a girl's head if we're talking about only one girl and girls' heads if we're talking about more than one girl. Of course, it's also possible to say a girl's heads, but in this case we're assuming that the girl has not one but several heads! Maybe, she literally has several heads (scary!) or she's just holding a bunch of doll heads in her hand or something to that effect. So, there's nothing surprising here, just standard English grammar.