Deflector beams must sweep ahead of the ship in order to clear debris out of the ship's path, so they must by necessity need to travel faster than the ship.
If they can do it, why can't phasers?
Although the general assumption is that the navigational deflector operates at warp, I think that, realistically, it would make more sense if it were only used at impulse. According to the theoretical warp-drive models that physicists have come up with, the warp bubble itself would "catch" debris, which would build up along the forward edge of the bubble like dirt and bugs on a windshield. And when the ship came out of warp, all that dust and debris would be accelerated forward with enormous kinetic energy, which means it would probably destroy anything directly in the ship's path. So you'd never want to come out of warp pointing at anything friendly. (In which case, who needs phasers?
