surely the dog having its back broken was a freak accident, and if it had been on a flat collar, it would have been its neck!
- our trainer recommends harnesses and halti type leads for particular dogs to start with, if the owner is really struggling for control - but they are gradually trained off them. We used harnesses in class for a few weeks when ours were puppies, but they now walk beautifully on their slip leads... in class! Heel work is something you do in a hall only apparently!

I'm sure with more patience and practice it might filter through to the real world too!
Ultimately the puppy is yours, and if you feel that a harness helps you in your day to day walks, then that is your decision,
Good luck with the training!