The reason that dead bodies are wrapped in plastic is to prevent the leakage of any bodily fluids that may escape the dead body while it's being stored or while it's in transport.
When a body is removed from a hospital or from a car accident, murder site etc then the body is placed into a body bag and the coroner or funeral home comes and gets the body.
The body can then be taken to a morgue or to a funeral home.
If the body has came from a car accident or a murder crime scene then the coroner will take the dead body to a morgue in a body bag and then they will be wrapped in plastic.
The body bag as well as the plastic helps to contain body fluids to make it more sanitary.
Then the body is put into a freezer in the morgue to keep the body from smelling.