I agree that it depends on the nature of the relationship. Sometimes they can and should be friends, and other times friendship is a terrible idea.
The problem comes when people think they SHOULD be able to be friends. Maybe they were friends before things got romantic. Often times, they'd be better just to split completely.
And offering someone friendship as a consolation prize ("Sorry, I no longer feel that way -- let's just be friends") is often ends up causing more harm than good.