This is so overly simplistic that it shows a complete lack of understanding of:
A. Transgender people
and
B. Sport.
1. Nobody chooses to be transgender. So your response is "All trans women should be banned from all women's sports." That's not what you seem to think you are saying, but it is what you are saying. "Wants to transition" shows a basic lack of understanding. How would you feel if somebody called you "sir"? You might be like me and not particularly care, but it's more likely that you would feel deeply uncomfortable. I have a cis woman friend who gets misgendered a lot because she has a name that people think of as masculine and it sucks.
2. Testosterone is not an advantage in all sports. Some sports are gender restricted that really don't need to be. In some cases I am fairly sure the gender restriction is not to protect women, but mens' egos when women beat them in, say, rifle shooting, where if there's a biological advantage, it's in favor of typical females.
3. Medically transitioning reduces those physical advantages. A trans woman who has been on estrogen and testosterone blockers for an extended period of time loses performance substantially. It is unfair to ask her to compete against cis men.
4. Cis women, with the most famous example being Caster Semanya, have been caught in the web of fairness focusing around gender.
5. Elite sports aren't fair anyway. You have to have the genetics and the body type and choose a sport that your body fits. I know you might make the argument that in that case trans women can pick a non-segregated sport, but it's not that simple. Elite sports are *never* going to be fair. You have to be built like Simone Biles to be a gymnast.
6. If somebody has transitioned young and used puberty blockers, the gender advantage is minimal at best. And again, *not in all sports*.
7. Some of these rules, although not all, force trans boys and men to compete against women. Which if they've been on T...
But the most important thing here is: Elite sports are never going to be fair. Letting a few trans women compete as women (and there aren't that many) doesn't materially change that.