There are physical differences in body structure between any two individuals. Michael Phelps has long arms. Is it not unfair that someone born with short arms has to compete against him?
Not having gender separated competition would probably decimate female sport participation in quite a lot of domains.
The short armed argument that you actually raise is more interesting. There are weight classes in boxing, and there could probably be arm length classes in swimming as well, but other physical differentiator that would take the place of arm length. I'm not really able to conclude on anything, but have feeling that the physical and cultural gender difference is large and important enough that it is prioritized, while arm length for instance is not.
In (edit: some) highly competitive physical sports there would be no person below median height at all in the olympics for example.
We can slice and dice all sorts of extremely visible inborn characteristics that will over time hopefully have just as much cultural relevance as sex or gender, as the cultural relevance of sex and gender decreases [0]. As that happens, we’re going to have to reevaluate what we culturally look for in sports. At the amateur level, hopefully this isn’t too hard, but I have no idea whether it will make professional sports more or less accessible.
[0] While height is mostly out of your control, it’s still unclear which of the kids in tryout team will end up tall enough to compete. That’s where sex and gender are more of a clear split, because you know most of the kids on the girls team won’t end up on a men’s team, so the split remains stable as they grow up.
That's not true for all sports. Gymnastics is highly physical and favors short people. Likewise, wrestling and Judo favor people who are short for their weight.
I do think height classes would make sense in basketball though, just as we have weight classes in combat sports.
See https://www.britishhorseracing.com/about/handicapping/ "Around 60% of all of the races run in Britain each year are handicaps. These are races where the Handicappers try to give each horse an equal chance of winning by allocating them different weights.
The highest rated (or ‘best’) horse in the race is given the highest weight to carry; and then inferior horses will carry lower weights.
For most owners, handicaps offer their best chance of winning a race. Without them, the top horses would almost always win and there would be no point in owning anything other than a top horse."
Now obviously that’s a dumb example, but why would it be interesting to see olympic sprinters beat Usain Bolt in a sprint if Bolt has a 10 pound vest on? I feel like the challenge at that point is determining how much to handicap everyone, and all the results would tell you is if you handicapped them correctly or not.
Some people are better than others. Sport is all about determine who is best.
The categories of world-class sport should really be "women" and "everyone." If women want to (and have the physical ability to) compete in "Men's" sports, they should always be allowed to - unless they dominate in a particular sport, in which case a special exclusionary men's version should be created.
That being said, we do have both the Special Olympics and an enormous number sports organizations of segregated by age and geographic location. You can start a swimming championship segregated by arm length, but people probably won't like it enough to watch, which is the real point. It's entertainment. Women's tennis is better to me because women don't serve/hit as hard, therefore more returns and longer exchanges. That's got nothing to do with "fairness."
https://boysvswomen.com/#/world-record
TL;DR at about 15, high school boys with proper training can compete against female Olympic athletes and win.