And an advantage of cutting them down and starting from scratch is that as they grow you can experiment with minor variations in the shape and as they get longer you'll find the exact length that works best. Once in a while when I feel I'm not getting the most out of my nail shape and length I cut them very short and do this.
Also, about shortening a damaged nail: it's tempting to try and salvage as much nail as possible, often leaving a small portion of damaged nail intact. Problem is that this causes a weak point in the nail and it is more susceptible to cracking, breaking, splitting etc. The best thing to do is remove every bit of damage and then a tiny bit more to insure the nail grows out strong and healthy, as quickly as possible.
One Ring to rule them all, One Ring to find them, One Ring to bring them all, and in the darkness bind them.