I mostly use a collar only, especially since Ruger outgrew his harness. While I do agree that a harness is a good idea, and I'm looking for another one, some trainers recommend a collar when training because the dog feels some resistance when he pulls.
Collapsed Trachia is a genetic condition which has nothing to do with using a collar, although I have seen people pulling so hard on their dogs it looks like their little heads are going to pop off.
If this is you, yeah, get a harness.
BTW, IMHO your dog should have an ID tag on at all times. You can put a harness on over a collar, and the average person who finds your dog hasn't got a clue about chips.