I think it is the parents responsibility to take care of their own children. If the parent wants the child to have an ID bracelet with their mobile number that's fine, but I don't think it's Disney's responsibility to provide it.
As far as babysitting goes, even though that is probably not what the original poster suggested, that would more likely happen. Parents become complacent(sp) and figure if something happens or my kid wanders off they've got the bracelet on and a cast member will call me.
Some people think that just because they are at Disney, Disney has to provide everything for their children. Grow up people, you had the little carpet munchers, you keep an eye on them.