the Enterprise and at least “12 like her” were refitted for 5 year deep space exploratory missions
That assumes the Enterprise wasn't the only ship on a 5 year deep space exploratory mission. Considering Kirk made a big deal about it in TMP it sounds like something only he and the Enterprise did.
That may be true, but it's an assumption that Roddenberry and almost everyone else has made, and since you brought up TMP, Roddenberry's novelization of that movie makes it clear that there were
other ships on five year missions.
I know the novel is not "can
n" but if the creator of star trek, "Great Bird of the Galaxy" himself thinks so, then that's good enough for me.