Obviously, this is a hero origin story so it would be pretty pointless for Strange NOT to evolve into the hero of the tale.
However, essentially, he learns from The Ancient One that the universe does not revolve round him, he gains perspective and lets go of his previous selfishness.
There is a conversation...
AO: You have such a capacity for goodness. You always excelled, but not because you crave success,but because of your fear of failure.
SS: It's what made me a great doctor.
AO:It's precisely what kept you from greatness. Arrogance and fear still keep you
from learning the simplest and most significant lesson of all.
SS: Which is?
AO:It's not about you.
Having learned that there is a wider universe around him and the fact that he is/could be a major player in it, "failing" takes on a much wider meaning than just being unable to perform surgery.
So he continues to excel, this time as a hero because the stakes are now so much higher.
Further, when the discuss Jonathan Pangborn (of the crippled legs)...
AO: He uses magic to walk. Constantly. He had a choice, to return to to his own life
or to serve something greater than himself.
SS: So, I could have my hands back again? My old life?
AO: You could. And the world would be all the lesser for it.
Finally, he realises that he could still heal his hands but there is still more he could do...
SS: You said that losing my hands didn't have to be the end, that it could be a beginning.
SS: Because there are other ways to save lives.
AO: A harder way.
SS: A weirder way.