So back to the OP. Two words: Doomsday Machine as most dangerous enemy. Eats planets. Neutronium hull. Phasers bounce off.
I'd like to see Kirk & crew take that on without the Constellation hanging around.
And that's how you send the Nu-Enterprise out in glory and bookend the movies: Kirk piloting the Enterprise down the throat of the Doomsday Machine while the crew evacuates in shuttles.