I know eh...I cant remember seeing bellybuttons on other animals...but then again I never really looked
Cats bite them off and then will eat it along with the placenta then lick their bloody vaginas clean. They usually have a litter too ... I think some human cultures actually eat the placenta as well but don't quote me on that.
I think your theory on aliens and the correlation to umbilical cords is correct. It tends to happen when the offspring hits about 13 and their body is taken over. The Aliens depart after doing the damage they need to, usually within 7 years. In rare cases, it is not an invasion that is a reversible process.