Well, it was cheaper to pay them for just the voiceovers, which were probably recorded when they came in to shoot other episodes. Actually it's impressive that the producers of TOS were as loyal to their recurring cast as they were.
I think they wanted to have a sense of continuity of personnel. And, with the exception of Nichelle Nichols, they weren't day players. Kelley, Whitney, and Takei were all guaranteed to be in 7 of the program's first thirteen episodes and Doohan was guaranteed to be in 5 of the first thirteen.