I think they settled around Kirk, Spock, and McCoy as the three stars, with occasional bits for Scottie and Uhura. Chekov and Sulu were good for an “aye-aye” from time-to-time in response to an “all ahead full” at the end of the show. The fact that Shatner hardly knew a bit-player like Takei isn’t really all that surprising. What is surprising is the tremendous mileage that George managed to get out of a show that lasted 79 episodes in which he was a very minor player.
I attended a sci fi convention not too many years ago and not many people even bothered to stop at George Takei’s table.
His career was resurrected by none other than Donald Trump on Celebrity Apprentice.