I just re-watched "Where No Man Has Gone Before" and wondered why they killed off Kelso. I know, it was just a pilot and no guarantee that the series would be approved.
The same reason they killed Mitchell and Dehner. It's simply a function of the way '60s TV worked. They didn't have many ensemble shows; a lot of shows just focused on one or two leads surrounded by various one-shot guest stars. The classiest dramas of the time were anthology shows, and that was thus the ideal that drama producers aspired to; but shows with continuing leads helped draw in ratings, and shows with standing sets, costumes, etc. cost less to make. So a lot of ongoing series were designed to fit a pseudo-anthology model, with the regular characters getting caught up in the stories of different guest characters each week. You can see in the first season how the episodes tended to focus heavily on guest characters, whether crewmembers like Mitchell, Bailey, Riley, Boma, and the like or outsiders like Harry Mudd, Charlie Evans, the Romulan Commander, etc.
So Kelso was just there to be a friend of Mitchell's, someone whose murder would show that Mitchell had lost his humanity and become a danger to everyone. He existed only to serve that particular story and was never a candidate for continuation any more than Mitchell and Dehner were.