My dog Suzi logged 68 days on the trail last year and she never once had an injury. No torn pads, bumps, scrapes, strains, sprains, etc. She's a very active dog and I prepared her for this type of activity. She runs with me 4-6 days per week and swims for an hour 3-4 times per week. Some dogs aren't meant for backpacking but others are. I have her checked out by my vet after any trip over 3 days and she's always returned with a clean bill of health. My other dog Maggie logged somewhere around 30 days last year and she too had no injuries. Base your decision to leave your dog at home on their abilities and your ability to properly control your dog(s) at all times.
Yes, I'm for dogs on the trail but I do see the other side of the coin. There are a lot, A LOT of irresponsible dog owners who are giving a bad name for all dogs on the trail.