They didn't put in "what they wanted". They put in the "Big 7" regulars from the TV show and the films.
...There was no "Big 7" on the TV show, just the movies, and that's what they wanted to do. They had the freedom to change it up a little if they wanted to...
So were Uhura, Sulu and Chekov just extras -- like, say Hadley, Leslie, and Lemli -- or were they much more front-and-center in the series than the latter three?
The answer is that Uhura, Sulu and Chekov were much more front-and-center on the TV series and many times integral to the plot than Hadley, Leslie, and Lemli (even though Hadley, Leslie, and Lemli actually appeared
in more episodes than the other three, but that's beside the point). As someone mentioned above, the TV series also featured Christine Chapel as one of the "Big 8", but she didn't really make it into the movies, so the Big 8 from TV became the Big 7 in the movies.
Of course Kirk, Spock, McCoy, Scotty, Uhura, Sulu, Chekov, (and Chapel) were featured in the TV show.