The sports I mentioned already use weight and other classifications. So I'm not proposing anything new, or overly complicated.
Factors like bone density, muscle/fat ratio, height, weight, lung capacity, etc. are measureable and objective. I don't see why any sport could not have people compete based solely on their measurements.
Interesting how keep going on about the "advantages" of men over women, but silent about the "advantages" of equipment, and training. Take the US Olympic swim team for example. They have high tech and expensive swim suits that other teams likely can't afford. So much for fairness in sports.
We could definitely have sports delineated for a gazillion different measurements... but we don't because, as I said, it's inconvenient and counter-intuitive. I mean, we could also have all athletes eat identical meals, train on the same equipment, use the same training techniques, get the same amount of sleep, and drive the same vehicles to practice, wear the same socks, and so on... but it does get overly complicated despite you saying otherwise.
Conventionally, sports have been separated along basic biological lines of sex.
The reason why category for weight was added to combat sport is because within a short time it became clear that bigger males had a significant advantage over smaller males, regardless of their skill level. Ditto for men vs women.
Strictly speaking, we don't have absolute fairness in sport. It's not realistically possible. But we remove the glaring and significant advantages where possible.
"I don't see why any sport could not have people compete based solely on their measurements." - I assume you don't watch sports because your posts are so sterile, byzantine, and academic. Your posts come from a place of lack of understanding of fundamental concepts of competition in sport in the real world. If competitions were based on equitable measurements of lung capacity, bone density, height, weight, etc., you'd have a tough time finding a match between two people with similar enough measurements that the sport would collapse into obscurity.
Current classifications work very well for trans women. They fall into the male category of competition. No need for anything to change.