I would say that arguments about GRA and self ID are limited with regards to this case.
I think you are wrong.
Every single man who identifys as a woman, for a day, or like Andrew Miller/Amy George for years is protected under Gender Reassignment. That's whats allows him to determine which pronouns he gets address with in court.
In the Equality Act, gender reassignment means proposing to undergo, undergoing or having undergone a process to reassign your sex. That is, in part, the process to begin getting a GRC. Theres a good chance he had a passport and driving licence in his female name. He certainly could have them if he wanted to.
Because the GRA exists, the PC of GR needs to exist to allow these men to gain the proof they need to get a GRC and a female birth certificate. But these men can get passports and driving licences and be recorded as female for years before they do, if ever get a GRC. And in the meantime, they can switch between male and female when it suits them.
Because the GRA and PC of GR exists as they do, children are been told that men who dress as women, are women.
If the GRC didnt exist, men wouldnt need female id, courts wouldnt call men women, men wouldnt be in female spaces, children wouldnt be told that men in womens clothes are women.
It could have been bad lighting and noisy, but how sure can we be that the girl thought she saw a female woman or a man shes be taught to see as a woman?