You're grossly exaggerting her damage. One portion of the aft starboard quarter of the saucer was opened up, one breach to the starboard side of engineering, the outer casing of the starboard nacelle, parts of the casing of the port, damage to the impulse deck and a misalignment of the warp core.
The hull breaches were only so deep, and the critical components of her were intact throughout. The black hole in the last film caused shipwide stress fractures and the loss of all 6 dilithium chambers, not to mention nearly burning the nacelles out.
As we see at the end of the movie, they've only had to work maybe a month, two at most, to repair her and even fully replace the impulse drive. Obviously they not only work fast, but can patch up that kind of damage with little effort.
Losing an entire nacelle, half the saucer, maybe the deflector assembly or a massive burnout of the entire warp drive might prompt another think about reactivating her, but apparently her repair was a breeze for them.
And the line about "nearly a year ago" is Kirk referencing him taking command of her for the first time, the epilouge in the hospital is two weeks later, the start of the 5 year mission only a month or two.