Wikipedia says the role was first offered to soprano Marie Roze, who declined. This web page
says Roze was thought to be Bizet's first choice. This site
says she called the opera "scabrous" (no source cited).
But the lady changed her mind. This site
says: "Marie Roze, who had earlier declined the role as 'scabrous,' played it to great acclaim in San Francisco." In fact, Carmen seems to have been one of Roze's two most successful roles, the other being Marguerite in Faust
. Now, if she could handle Marguerite's high notes and Bizet did indeed want her to sing Carmen, would he have written it for mezzo voice? Lots of iffy stuff here.