Is there any reason other than staying clean?
In: 5
Washing your fingers also causes the fibers from the filed nail and sub cutaneous nail to spread out like a fan. Now you file again and get smoothly filed nails.
Eli5: Why should we wash our nails right after cutting?
That is pretty much it. You are exposing more of the germ collecting crevices and cracks that was otherwise protected by longer nails. Now go get some antibacterial soap in there!