Re: So, do we know why Goldsmith chose not to use Courage's theme?
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.
A quote from Courage but not from the TOS theme. The very short cues we hear during Kirk's monologue before the theme music is the one that's basically become the Star Trek theme, but the theme itself has only been used in TMP before the reboot, which is why I was pleasantly surprised to hear it over the end credits in 2009.
And that's my opinion.