It wouldn't look too good if the two big representations of racial diversity suddenly weren't there anymore.
Takei held out - till the day before principal photography began - on ST II, IIRC, and only signed when Harve Bennett promised the scene where Kirk tells Sulu he's to be captain of Excelsior. The scene was shot but cut.
Similarly, he was reluctant to sign for ST III, till they promised him a martial arts scene (although he initially hated Sulu being called "Tiny"). His ST III appearance was also tied to Takei running as Paramount's representative with the Olympic flame, IIRC. Great publicity!
Similarly, Takei held out till as long as possible on ST IV, until Harve Bennett promised a scene with Sulu's ancestor (the child actor was difficult and, with failing light, the scene was rehearsed but never filmed.
For ST V, Shatner personally negotiated meaty "pensions" as part of the main casts' contracts, to help compensate for how Trek had helped to typecast them. (And probably because Shatner knew they all originally had reservations about his directorial role.)
And, of course, for ST VI, Takei was finally Captain Sulu.