Isn't it on the side wanting bans here to show that trans athletes have an unfair competitive edge?

I don't know why we would start with the assumption they do. If you ask good faith researchers in this space, the truth is that we don't have robust data on real world competitiveness.

You can't just say that because cisgender male athletes have a performance advantage over cisgender women then trans women do. What lab data we do have indicates trans women have notable differences from cisgender men. And this is important. As even within cisgender women you have large differences on these factors in these lab studies- say cisgender women with PCOS for example- and obviously those women aren't excluded. And the limited real world performance studies we do have are mixed.