"Bald as a coot" is a saying which seems to me to be a bit unjust to the Eurasian Coot. In the United Kingdom this bird is even known as the Bald Coot.
The "baldness" is actually a white shield extending from the bill up the front of the bird's head and serves for protection and display.
I'm sure coots are proud of them. I've never yet seen one with a comb-over.