Batman could escape the pit because he got proper moral guidance from the prisoners. They made him understand what it takes to leave the pit successfully. But it seemed they never wanted to leave the pit. Why is that? If they knew the principle to success very well, why did they not try? This is obvious from the movie, they were not well in that pit!
Indeed the other prisoners (or some of them, the younger ones maybe) still try to escape from the pit, they just don't make it. There is a scene where one tries to escape while Bruce is still lying paralyzed.
Now the doctor could tell the others the "secret" of escaping (which I'm not sure he ever did). But in the end, just leaving away the rope is not enough, it is more of a mental stimulation. You still need the will and hope to escape and you still need the physical abilities (while Bruce was getting older and had his problems physically, he wasn't one of those hopeless failed existences imprisoned for years down there).
Even if the doctor had ever told the "secret" to the others, they probably were just too hopeless and desparate to try the climb without the rope and risk the rest they have of their lives. And even if they did, they either didn't bring the needed physical strength or, even more probably, the needed mental strength and the will and determination to escape and survive, having their will and hope broken after such a long time in the pit.
In the end I'm not sure the doctor was that aware of this "secret" of escape at all. It wasn't just about leaving away the rope, you still need a will as strong and determined as that of Bruce. And only when seeing such a character in Bruce the doctor realizes that there is finally someone after the kid who could make it out of the pit and he gives him the final stimulation he needs.
Those who had the heart and really willed to escape did try, but sans success. This is clearly shown in the scene where Bruce is bed ridden with a broken back and a man tries to escape but eventually falls, banging into the wall several times and then going limp.
Moreover, Bruce was guided and supported by two very old and frail men, none of whom could have themselves taken the leap.
I would say that all of the prisoners had lost hope about escaping. Apart from Bruce, we never see anyone trying to climb out of the pit during his stay in prison.
However, I am sure that Bruce's escape inspires prisoners who will take the challenge of climbing it after.
This would be in resonance with one of the roles of Batman in Gotham City, which is to give hope to the "small people" living here.
Indeed, we see children smiling when they understand he is back, also the feats of Batman seem to inspire the character of John Blake into becoming a vigilante hero.
Bruce Wayne / Batman is an inspiration for everybody !