On a pedantic note, it should be said upfront that he did use it, as an underscore to the Captain's Logs throughout the movie.
Well, technically, he brought in Alexander Courage himself to arrange his own theme for the captain's log segments (rather than just conducting it as you said).
I was wondering though, has Goldsmith ever expressly said why he decided to do this, rather than just using an upscaled version of Sandy Courage's TV theme music? Was it a design choice on his part? Did he decide that it suited the movie better to have it's own theme, a more rousing and completely theatrical theme tune rather than the one heard on TV?
Well, it's not like there was some longstanding tradition of movie adaptations of TV franchises using the same themes the shows used. Even the 1966 Batman
movie, made during the run of the series by the same producers and with the same composer, had a new main title (although it did use the Neal Hefti theme motif at some points within the underscore). And all the Trek sequels only quoted the Courage theme briefly at the start of their main titles before going into their own original themes -- with each different composer creating a new theme, and Goldsmith creating a different theme for each of his TNG movies. As you mentioned, the TMP score did homage the TOS theme to about the same extent that the others did; it just did so in the body of the film rather than in the titles.
So I don't see it as something that needs any special explanation. Sure, it later became a tradition to open the main-title theme with a quote of Courage, but it hadn't become one yet at that point, and I think that's all the explanation that's needed.