Was it just for a cool FX or is there some solid underlying physics.
My take is that those are not stars, but instead were particulates of interstellar matter that the main deflector was moving to allow the ship's passage, but were still close enough to pass through the outer portions of the the ship's warp field/bubble.
Being caught in the deflector and passing through the warp field made them visible.
In only one TNG episode (WNOHGB) do we see the Enterprise at warp from the side, from a distance. And the extent of the "streaking stars" there could be explained by size of the ship's warp field. It's fullest extent could reach for miles (stronger near the hull).