The premise here is incorrect. Roddenberry originally intended TOS to be more of an anthology show. Shatner and Nimoy were the only regulars in season 1, but the rest of the ensemble was meant to be get a lot of focus, as is evident in early episodes like "The Corbomite Maneuver" and "The Man Trap." Indeed, Yeoman Rand was originally meant to be about equal in importance to McCoy; look at the early first-season end credits and DeForest Kelley and Grace Lee Whitney are credited together on the same title card. So it was meant to be Kirk first in importance, then Spock, then McCoy and Rand, then Sulu, Scott, and Uhura -- but with the goal being to spread the attention around to cover the whole ensemble. (Keep in mind that "This Side of Paradise" was originally meant to be a Sulu love story, which is why the love interest has the "exotic" name Leila Kalomi.)
But then female audiences went gaga over Spock. He became the breakout character, with Leonard Nimoy getting more fan mail than the rest of the cast combined. So the network pushed for a heavier emphasis on Spock. He was now the de facto star of the show. But Roddenberry and Shatner both intended Kirk to be the star of the show and fought to keep it that way. Eventually, Roddenberry's friend Isaac Asimov (always a smart guy) suggested that if Spock was going to be the breakout star anyway, the best way to keep Kirk central was to emphasize his friendship with Spock, to make them an inseparable team. So that was how Kirk managed to stay at the heart of the show. And McCoy also managed to stay front and center because he was also closely connected to Spock through their rivalry. And that's how the show ended up being focused on those three characters at its core. But because it was now so focused on Spock and the two men closest to him, the rest of the ensemble got marginalized more than was originally intended.
It's not uncommon for a show to start with an ensemble approach and then focus on a breakout character while the rest of the ensemble gets marginalized, often to the point of near-invisibility. There was Dr. Smith, Will, and the Robot on Lost in Space; Fonzie on Happy Days; J.J. on Good Times; Urkel on Family Matters; etc. Not to mention comic strip characters like Popeye (introduced 10 years into the run of a strip about Olive Oyl and her boyfriend Ham Gravy), Nancy (originally a supporting character in Fritzi Ritz), Snuffy Smith (supporting in Barney Google, who continued to be nominally included in the strip's title long after he'd all but vanished), Dagwood (originally just one suitor in the strip about flapper Blondie Boopadoop's life as a swinging single girl), etc. It's surprising how common this was in comic strips.