If the surgeon is experienced in obtaining good local anesthesia and the patient desires sedation and is not too anxious it can be safely done with iv sedation. I have done many, and they have gone well. Patient selection and close cooperation with the anesthesiology team is important.
Breast reduction is not usually performed under local with sedation. It is a long procedure and even when the local is working perfectly, it is hard to sit still for hours with no bathroom breaks while the procedure is performed. There is a limit to the amount of local that can be given, so general anesthesia with a board certified anesthesiologist is the way to go.