That one-shot character was the means to explaining a great number of things.
If Gary Mitchell never existed, Star Trek would be exactly the same. The events in WNMHGB had no effect on the rest of Star Trek on-screen history.
Even Mitchell's revelations about Kirk -- that Kirk was a tough instructor and very studious -- never came to light again in the series, and did nothing to define Kirk's character as we came to know him.