Certainly TWOK could've been written to provide a meeting or confrontation between Kirk and Khan, but I am a loss to say how that would've pulled that off in the confines of the film/story that we got.
But that's the point. They didn't have to tell the exact same story. They made it up, after all. There were lots of possible stories they could've told.
As for hurting Kirk, it didn't have to be solely physical pain. Khan realized that Kirk was goading him, that Kirk wanted him to beam down to the asteroid so he didn't. He understood at that point that he could wound Kirk more deeply by killing his friends and destroying the Enterprise while leaving Kirk stranded and helpless to prevent it.
Again, whether you can rationalize it is beside the point. I do understand the characters' motivations in story. I'm not talking about the characters. I'm talking about the actors
. I'm talking about my regret that I didn't get to see the actors play off each other.