As others have pointed out...there are several reasons why the mask/costume ended up being what it is.
Mainly though, the simple answer is that Wes loved the mask and thought it was perfect. The script described the killer as wearing a ghost mask. But nothing else. Its been said that Wes asked Kevin "What else does the killer wear?" and Kevin didn;t have an answer and Wes explained that if the killer just wore a mask, then the audience would be able to tell who it was just by their clothing.
So they had to design a costume that completely covered the persons body.
Also the name of the costume in Scream 1 is "Father Death". Wes said that he chose this name as yet another red herring. The goal was to throw the audience off even more, by further pointing the finger at Sidneys father...."Father Death"....