It's for more than just medical info, though. It's so emergency responders can have the information to contact someone about a child who may be uninjured or mildly injured in case the adults in the car are all incapacitated or even killed.
Think of this way - if you get a crash and die, do you want your severely traumatized kids waiting for six hours while strangers (granted, very nice strangers) figure out who they are and who to call to come get them, or would you prefer that their Gramma (or Auntie, or whoever) show up in an hour? It's also very useful to have them on the carseats that Nanny or Grandparents use for your kids. If Grandma has a couple of boosters that she uses for five grandkids, you can still fill out the info in a generic way and be assured that one of the parents would be called, yk?
I agree it's not a perfect system, though. I transport my friend's kids in my car with my seats once or twice a month, and since my seats have my kids' info on them, if we got in that kind of crash, there would be some confusion.
Still, now that I think about it, if they called my mom and told her they had her grandkids, and she showed up and it was actually my friends' kids, she would still be a familiar face, plus she'd be able to provide contact info for their family, so still a positive result. And I'm sure emergency responders are aware that the system isn't fool-proof.