It seems pretty clear in the initial instance that the Enterprise was conceived of as being on a fairly normal tour of duty, that five years was a pretty standard length for a "patrol" of that nature. The notion of its mission being somehow "special" came AFAICS with all the later inflations of the Enterprise into the Most Important of All Ships and Kirk into the Galactic Gary Stu instead of just one ship captain among many.
No, it's just common sense. That tour may be one of the normal mission profiles for that particular class of starship, but that doesn't mean it's the only kind of mission Starfleet ever does. If anything, it's just the opposite of inflating the Enterprise
into something special, because it's rejecting the impulse to treat the Enterprise
's mission profile as the template for all other starship missions, treating it instead as just one type of mission profile out of many. It makes Kirk and the Enterprise
less exceptional, not more. After all, nobody's saying it was the only
ship that ever went on a 5YM, just that 5YMs aren't the only type of mission in existence. As with most things, the truth is probably between the extremes.
I mean, even TOS gives evidence that not all Connies are on 5-year missions all the time. Look at "Where No Man Has Gone Before." A mission out to the edge of the galaxy and beyond is something that would take months as a round-trip journey, and thus is likely to be a dedicated mission of its own rather than just something inserted into a 5-year tour. The fact that the ship underwent a major refit between then and the first season further suggests it was part of a separate, shorter mission before the 5-year patrol began.