Off topic, but is there such a thing as pairs gymnastics? That would be cool. So would trapeze as an Olympic sport.
About all-male pairs teams in figure skating, a few years ago there was a mixed team (one man, one lady) in the sport of synchronized swimming. All the two-lady teams said that wasn't fair, because (a) the man, being taller and stronger, could do more impressive lifts, and (b) the team could do more touching and striking of quasi-romantic poses.
On the negative side, they did not look like two peas in a pod for unison work, in comparison with all-lady teams.
There is a very good all-female ice dance team in the Detroit area. They compete in the gay games and have won a lot of prizes.
My school has a "shorties" basketball team. The tallest you can be is 5 foot 8 inches. If you are taller than that, then you have to go out for the real basketball team. This is a lot of fun for the participants, but not very many spectators come out to see their games.
My home town (Spokane

) has an annual marathon. It started out with just some neighbors getting together to run for fun. Over the years it grew bigger and better and eventually attracted some sponsors and started awarding cash prizes.
Then some Ethiopians showed up. Hey, no fair. Obviously the Ethiopians are going to win all the prizes, and we locals will be shut out of "our" race. Many citizens wanted to limit the race to residents only. Others were willing to compromise -- the Ethiopeans could run but they would not be eligible for prizes.
The argument on the other side was, what is the purpose of holding a race except to see who can run the fastest?
For many years in college basketball the rule about black athletes was, you can play two at home, three on the road, and four if you get behind.
About whether there should be such a thing as women's figure skating, I think (we had a separate thread on this topic) that we have the CoP to thank for that question coming up in the first place. In the olden days it was obvious that figure skating was half sport, half looking pretty. Women could hold their own because they were prettier. So much prettier that that real question was, why is there such a thing as men's figure skating?
So yes, age group championships, gender championships. little league baseball, the masters (over 50) golf tour -- it's all good.