She's not a Dame because the honours system is already disreputable ana to bestow a senior award on Ms Barker would heighten that disrepute.
Sue Barker was a decent tennis player, winning the French Open in 1976 and beat at one time or another most of the top players of her era, including Chris Evert, Martina Navratilova, Billie Jean King, Evonne Goolagong-Cawley, Tracy Austin, Virginia Wade, Maria Bueno, Rosemary Casals, Andrea Jaeger and Pam Shriver. She would have made an all England final in the 1977 Wimbledon tournament but unexpectedly lost to Betty Stove in the semi-finals and so lost the chance to meet Virginia Wade in the final.
Since then she has forged a career in broadcasting and good for her. But she has already been awarded an MBE (for services to sport and broadcasting) and an OBE for services to broadcasting and charity). That should be more than enough because to make her a Dame would be rather like making Gary Lineker a Knight.
Barker was appointed Member of the Order of the British Empire (MBE) in the 2000 New Year Honours[24] for services to sport and to broadcasting and Officer of the Order of the British Empire (OBE) in the 2016 New Year Honours for services to broadcasting and charity