The larger question is why don't men and women compete together in several competitive sports...
In competitive levels the following sports do not have men and women competing together (this is off the top of my head)...
Hockey, baseball, volleyball, beach volleyball, soccer, tennis, table tennis, football, water polo, track and field, rugby, Australian rules football, lacrosse, ringette, golf, gymnastics, broom-ball, basketball, cricket, cycling, swimming, wrestling, boxing, fencing, martial arts, billiards, darts, handball, squash, badminton, diving, rowing, weightlifting, skiing, luge. skeleton, bobsled, speed skating, snowboarding, ski-jumping, marathon, triathlon, lumber-jacking, archery, and polo.
When men and women compete together in these sports it become a spectacle or a marketing thing. Curling would be no different. It seems that we see more men and women competing together in things that have an artistic element like figure skating or dance where the differing strengths of the genders can complement each other instead of being thought of as a handicap.