The advantage is less friction, hence you don't need to pull so hard any more to get the leach tight.
You can buy tapered lines if you don't want to splice. Or you can make it by removing the core or by removing the outer braid or by splicing a thiner line into the thicker one, depending on the sheet construction.
Easiest and maybe most elegenat way is to have a rope with strong braid and soft core, where you can remove the core and still have the strength, eg.g Liros "Magic sheet"