Sorry - my bad. I was thinking of two size-scale ships at the same time. I'll try again.
If the Enterprise saucer-section was no larger than the 'football' ship... then no pivot is needed. But if the saucer is scaled larger then the 'football' ship... then pivot is needed to prevent the saucer's leading and trailing portions from extending into, and being destroyed, in the 'close' warp zones ahead and behind the warp-ring.
The 'saucer shape' is what the Enterprise uses as it's primary hull shape. And it might be desired/required to disconnect from the warp-ring, and land the ship (proper) on a planet. Perhaps as a colony base station.
OK, I'll try again as well. Why does it need to pivot? Just build it in the orientation that it needs to begin with. Why a saucer shape? Why not just build it in a more efficient shape to begin with?