ND filters used to only be used for daytime, when you wanted to show a longer shutter speed, like with a flowing body of water/waterfall. ; When you can't stop down your lens anymore or lower your ISO, that's when the ND filter had to come out. ;
But fireworks, since digital doesn't seem to suffer from the reciprocity effects[nb]A phenomenon where film actually needed more light than what a meter would tell you. ; Example, if the scene required 4 seconds of light, the film actually needed 6-8 seconds of light. ; It gets worse the longer your shutter speed is.[/nb] that film had, you can easily blow out a background element (like the castle) while not getting that many fireworks trails in your picture. ; So, with an ND filter, you can get more fireworks in a shot without blowing out a background element, and in most cases, reduce the exposure of smoke in the shot. ; The fireworks still show up because they are so bright.
Additionally you can use an ND filter to take longer shutter speeds in the day, which should result in blurred/invisible guests, say on Main Street, because they won't stand in one place (usually) to properly expose.