I would say the healing might take longer but I wouldn't say it would not take place because the therapist wasn't very good. If you don't put neosporin on the wound, don't have a medicated bandage and just work on it yourself; give it a wash and keep an eye on it, etc. it heals, might be lumpy and bumpy and take longer, etc. The broken leg will mend if you care for it yourself and don't get it casted, just not like you'd like it to, you might still have a limp, etc. because you only sort of got it straighter (not having the experience, skills, resources of a doctor) and the tools you used, the stick you found :-) weren't as good as they might have been with a professional looking at it.

I agree that with a not very good doctor you can end up with a not very well set leg that's slightly off and causes you pain, gives you a limp, etc.; that's why we get second opinions, research our doctors and illnesses, and educate ourselves as much as possible. But I don't think, even if you randomly pick 5 doctors, that they're all going to be equally mediocre? The chances of that are not good. If all the doctors are "alike" and my leg doesn't feel like it's healing right, I'm going to look at what I can do myself to fix that; I'm going to rest more, eat better, ask my friends whose opinions I value what they think, ask others with broken legs about their experience, etc.