The actual format of the original series (TOS) from 1966-69 was more centered around Shatner to start with. Look at the 1965 pilot "Where No Man Has Gone Before" and you'll see it. TOS wasn't exclusively the Bill Shatner show; Leonard Nimoy as second-in-command Spock was billed on the marquis credits with Shatner.
It wasn't until the show's second year that DeForest Kelley was also recognized in the opening credits as Dr. McCoy. All the other familiar faces were supporting actors playing what were considered background characters. Those characters (Scott, Sulu, Uhura, Chapel, Chekov) took on a life of their own as the show evolved.
The show still centered around Kirk, but that concentration softened quite a bit as these other characters became more visible.