Well the word 'bald' is actually derived from an old English word 'bala' which means 'white patch'. If you look at a coot, they have a white patch above their beak known as a 'knob' or a 'frontal shield'. It is this that has given rise to the term 'bald as a coot', rather than because they are featherless.

What does bald as a coot?

Meaning. Totally bald. An appearance of being completely bald, that is, without any hair on the head.

What does the saying bald as a badger mean?

Barbers use talcum powder, applied with a barber's soft brush, to loosen hair and make it easier to remove from a client's neck. The finest of brushes are made from badger hair, hence came the expression, 'Bald as a badger'.