I never understood why people liked Wrath of Khan so much? Of the original 6 movies, it was probably my second least favourite. I also felt that the villain (Klingon General Chang) in Star Trek 6: The Undiscovered Country was far superior.
"I am as constant as the Northern Star"
"Cry havok! And let slip the dogs of war!"
He also got the best lines of any Star Trek character that I can recall (and yes, he worshipped Will Shakeseare).
I think the main thing is the history that Khan has with Kirk. Other than that you are basically right. Also Spock sort of dies, in this movie as well.