I had this problem when I was younger. I was told by R’ Yitzchok Berkowitz that there is a problem with biting nails because of the tumah. What do we wash negel vasser for in the mornings? “Negel” means nails. The ruach ra’ah in the mornings settles on the fingertips, particularly the nails. That’s why you wash your hands. When you cut the nails off (either with scissors or your teeth), then there is a certain tumah that is with them. Just like you should wash negel vasser after a hair cut, you should also wash negel vasser after cutting your nails.
Sam2, I like your point about assuring things during the week just because you might do it on Shabbos as missing the point of making Shabbos different. We’re so much on autopilot that we can’t even force ourselves to be conscious on Shabbos and refrain from doing the issurim. Maybe we should try learning a little hilchos Shabbos on Shabbos to raise our awareness of the halachos.