I have removed a total of two coccyxes in my career. Both were significantly displaced, became better with injections and were quite painful with sitting. It is not a recommended surgery in general. You could visit a general surgeon who specializes in colorectal surgery to get another opinion.
Donald Corenman, MD, DC is a highly-regarded spine surgeon, considered an expert in the area of neck and back pain. Trained as both a Medical Doctor and Doctor of Chiropractic, Dr. Corenman earned academic appointments as Clinical Assistant Professor and Assistant Professor of Orthopaedic Surgery at the University of Colorado Health Sciences Center, and his research on spine surgery and rehabilitation has resulted in the publication of multiple peer-reviewed articles and two books.