I think that certain systems are introduced and then made obsolete by more efficient engines as time goes by. I think the warp governors on the NX-class and the impulse deflection crystals used by ships in the late 23rd-Century kind of fell into that category.
It's possible that the Galaxy-class may have impulse deflection crystals too--there's two large blue glowy areas above and roughly between the saucer impulse engines--or they might be something totally unrelated.
As far as power sources, I've always leaned to the idea that both warp and impulse engines are used to power a ship's EPS grid, but that impulse power is used as a backup to warp power, but also can be used for less energy-hungry systems aboard a ship as well.