I think you're falling for Sticker Swap Fallacy. The goal is to have fair match-ups in sports. Gender and sex are two possible labels to use to assist with this, but they're imperfect enough that we probably ought to not use them as the primary differentiator.
The solution is simple: class every sport like boxing.
Pick a sports-relevant metric and split into divisions. Some sports will naturally fall into gendered divisions, while others will have varying degrees of co-ed competition among competitors of similar ability.
The way out of this is not to pick a better scissor of sex or gender, it's to pick a better scissor of ability.
This "solution" can really only be proposed by someone who has not played sports. This would simply result in women being unable to compete in sports professionally, outside of a couple small niches like ultra long distance swimming and a couple sub-disciplines of gymnastics.
It really depends on the way classes are divided. Dismissing the general concept demonstrates a fear of change rather than a legitimate openness to fair play.
No it doesn't, and no it doesn't. Proposing this concept demonstrates a profound ignorance of what competition at the top level of sports actually looks like.
The concept is just bad, unless your goal is to prevent women from being able to make a living playing professional sports.
The thing is, we're already using a scissor for ability, just a poor one with the exact problem you describe - it renders trans women unable to make a living playing professional sports. Throwing one group under the bus for another cannot be avoided so long as sex or gender are part of sports divisions.
You are clearly out of your depth. Have you ever competed in high level sports? Please don't speak on things you know nothing about. It takes a lot of gall to tell someone 'please let go of the need for this' when they are pointing this out. I will do no such thing, but I likely will give up trying to educate you.
I won't respond further unless you pick an example sport, and propose how your "scissor for ability" would work, in concrete detail. If you do this, I will be happy to explain why this would result in neither women _nor trans women_ having any chance to make a living as professional athletes.
Men are stronger, faster, have more dense bones, have bigger lungs, bigger hands, etc, etc, etc. Men and women are different in hundreds of ways it's not just 'lean body mass'. Men are better at sports than women. Do you even live in reality? Have you ever completed in anything in your life?
Pick a sports-relevant metric and split into divisions. Some sports will naturally fall into gendered divisions, while others will have varying degrees of co-ed competition among competitors of similar ability.
The way out of this is not to pick a better scissor of sex or gender, it's to pick a better scissor of ability.