Could you please explain what rule do you use when you make "double" words like babysitter, headhunter, songwriter, calorie burner?
Why is the first word singular? Not babiessitter (If it means a person who sits with not only one, but with many babies)? Not songswriter? Something like body builder is singular because you have one body, but why are the others not plural?
You can change position and say "writer of songs", and now it is plural. It is because it would be harder to pronounce?