I think you're right Rage, it would depend on the person. You wouldn't want anybody to feel that they'd missed out by dancing with somebody of the same sex (feel they hadn't had the 'traditional' experience iyswim), but if they were keen to then it would be good to see. I don't know whether you'd be more likely to get men or women wanting to do it.
Anecdote warning, but...
I have never met a man (gay or straight) who wanted to dance male/male competitively. Practically everybody will muck around and dance same-sex or reverse role at social or party dances, so it isn't that they haven't tried it (sometimes just for the fun of seeing if somebody 5'2" in heels can lead a 6'+ man!). But when it's being done 'seriously' there's no appetite for it, because they all want to lead! Perhaps all the men I know are just bossy and like to be in charge. 
(Actually, being fair to them, a lot would say that it wouldn't be fair either. In Strictly where you're not all on the floor at once it isn't a concern in the same way.)
Interestingly, when I danced at university, beginner girls would sometimes choose to pair up because they could pick the steps up more quickly than the boys and could improve faster! Girl/girl partnerships also often had quite a fun vibe with choosing matching dresses and doing each other's hair and make-up to match, so it was something you could do with a friend.
I've always had male partners, but at times have definitely thought that dancing with a girl might be easier — personality-wise if not dance-wise!