the problem boils down to this... what will you do if one leg refuses to let your pet continue? What will happen if you depend on them not checking something and then they check and your dog is grounded?
I would like to say that we check several airlines before moving to Israel and many of them would allow a small enough dog I E. our basenji, in the cabin but they limited the number of pets most of them at around 3 per cabin and they would say that if someone flying who was allergic then your dog or pet had to go in the hold so you didn't really know till you got there. We were lucky to have 2 pets that could be next to each other and they both just sort of chilled and even though it was a hellish flight neither of them seemed at all stressed or bothered and we were able to keep them with us until they actually took them to put on the plane and pick them up almost immediately on landing. I just think unless you're moving the best thing for your pet is to find a way to leave it at home. If you must take the pet then you may be better off paying the extra to have a professional pet travel agency take over all the responsibility and fly your pet for you which unfortunately doesn't usually include in the cabin.
I never had an issue flying puppies to their new homes in the cabin with their new owners.