I'm not exactly sure how much of TOS's popularity was driven by character development. I think that Star Trek, like its sister show Mission: Impossible, was largely plot-driven. But I'm sure Kirk must have grown and developed substantially between "Where No Man Has Gone Before" and "Turnabout Intruder."
There may have not been much growth for Kirk (although there was some; Spock had much more development over time) but he was at least an actual character with wants, desires, and a smidgen of a personal life. The characters on Mission: Impossible were ciphers; after two seasons, Nimoy notes in I Am Spock that the only time anything was learned about Paris was a single scene in which he entered a room wearing a tuxedo.