What's the point of Bitcoin eaters?
I'd assume it's just so people reading the docs won't try to "tip" the writer and send to a foobar address that was made up for the sake of example


That is correct! 

Other than that, there is no other real point at all. These bitcoins are gone forever and no one will ever be able to get them. 

However there is some projects or new coins that does Proof-Of-Burning and by sending the bitcoin correctly to the bitcoin eater address you would get corresponding amount in the new cryptocurrency.