The OP seems to have misunderstood the purpose of the single sex exceptions.
Oh dear, oh dear.
Seems many have failed to read the OP and the point I was making.
So one more time, and as has already been said here and on numerous other threads (and in fact as said by EHRC)
If the GRA had not been intended to create the concept of someone being a "legal sex" as opposed to an actual biological sex, there would be no need to SSE.
It is BECAUSE those drafting the changes to the EA to allow for those with a GRC to be treated as though they were through a certificate the same as those born a sex, that the SSE had to be created.
This needs to be spelled out, that for all those arguing that the then Government (Labour) never intended legal sex to be the same as biological sex, in fact as both the EHRC and as I quoted Lady Haldane, have interpreted the law, FOR ALL PURPOSES those with a GRC are legally entitled to be seen as the opposite sex to the one they are born.
And because this the intention, as a very generous (sarcasm) the queer informed writers of the EA thought, goodness me, maybe, just maybe there are occassions (such as Rape Crisis Centres) that biological women would (and we have to admit they may even be entitled) be allowed to exclude "legal women" with a GRC.
This is what this court case is about. Did or does the law as written, mean that "legal women" are women.
So whether you or I, or the EHRC (please re-read their comments in the OP) think this is wrong, the fact that the SSE were written is because those writing about the protected characteristic of sex ACCEPTED (and wanted) those with a GRC to be taken as having actually changed sex.
This is why some of us are questioning how this court case can change written law.
If a GRC was not intended to mean someone became legally the other sex, then there would be no need for SSE, because sex would still mean, and only mean, biology.
None of us may want this to be the case, but that is what it is.
FWS are using the court system to challenge this because it is not only wrong, but as has become increasingly clear, impacting on women's sex based rights. So even if they win, will the law be re-written?
Others chose to petiton Parliament, and as a result there was a "Westminster Hall" (actually a small committee room) where various MPs discussed it.
The outcome of that was that the then Government said they would do more work on clarifying the law.
This is what Kemi Badenoch was doing up until the moment the Sunak called a snap election. If he hadn't for all we know by know she would have presented to the HoC by now a solution to the wording of the EA. (I doubt she would have attempted to change the GRA)