Folks who want to take dogs hiking don't think about what if the dog gets hurt... I've run into people trying to carry out dogs that tore up the paws walking on open granite.
Dogs need to be conditioned for the task, same as people, and you'd also need to train the dog to come reliably and not chase animals, including other dogs, stock, people, etc. Then you need to train the dog to sleep in the tent without tearing it up to get outside for some reason. Then you'd need to train the dog to carry the pack with its food, and if something happens, you get to carry the pack and the dog along with your gear.
And yes, national parks do enforce the no-dogs-on-trails rule - seen people hiked out of the backcountry and fined for ignoring the rule.
I do know hiking dogs - some of them are great on the trail, awesome companions, very well trained not to drink or eat until told to (did you know dogs can get giardia?). But it's a lot of training and conditioning to get them that way.
"In the beginner's mind there are many possibilities. In the expert's mind there are few." Shunryu Suzukihttp://hikeandbackpack.com