The idea that it "cheapens the impact" is a nonstarter for me. I agree the script has plot holes. I agree that Khan was a poor choice. I think the space jump was dumb and the Scotty leaving the Enterprise only to return was equally dumb.
But, the idea of Kirk's sacrifice being cheapened is one I cannot begin to fathom. He goes from thinking he is above the fray, that the rules don't apply so long as he doesn't lose a crewmember, and cooks the book to support his ego. That at the end he has the same damn choice as his father, and chooses to sacrifice himself in the name of his crew, like Spock had done in the name of the Prime Directive, moves me every single time. Because it's Kirk's story, Kirk's choice and he doesn't know that McCoy will save him.
If he stays dead he will only know the ship was saved, but not the rest.
"Ain't it a bitch."