Mitchell: "I'll just keep getting stronger. You know that, don't you?"
Yup, he did know that. There was no foreseeable limit to Mitchell's growth and power. Mitchell had to die or else grow so powerful, anything would be possible for him. Even getting off the planet. Either Kirk would have to do the deed, or his last order would (hopefully) take care of it.
The real question should be, "why didn't Kirk just grab the phaser rifle when Gary was normalized and blow him away instead of having a brawl?" I mean, aside from "the episode had to end with a fistfight in a ditch."