Have you ever had a spine/neck injury? There is no amount of streching or yoga that will fix it. I fell rock climbing last summer and was in serious pain for weeks. I went to a physical therapist not a chiropractor, but "cracking" your back is necessary for some injuries and it is the only way to fix it. It took a hell of a lot of force to get my spine back in line but it feels better almost immediately. After that comes the therapy to rebuild the muscles, but that takes a LONG time, and resetting the spine is done multiple times in there.
Sure, strengthening back muscles is not enough for real injuries, but neither is going to a chiropractor. At best, the chiropractor is a physical therapist with a focus on the back. But mixed in with those people are a good number of others who believe in treatments with no basis in evidence. And at times, as gcheong pointed out, the treatments can result in making the condition worse.