I always thought the more elegant approach to all of this was to add a mixed sex league. Keep the traditions, add a novel new one, and let people consent to who they want to compete against and watch
In the sports I competed in, the men's class was really an open class. (EDIT: Looking at past results, we didn't even have a "men's division". There was just a separate women's division) Anyone could compete in it. The women's classes were the only restricted classes.
There are several sports where female physiology (skeletal structure, etc) has inherent advantages over male physiology where this may not be true, though.
That already exists. That’s the men’s category. There are no rules forbidding women from competing in men’s categories at Olympic events.