Women have the right to single sex spaces under law. There is an exemption clause to protect single sex spaces.
Why change the law?
Because its clear the law isn't being properly understood and is being misrepresented, because certain organisations don't understand the exemption clause properly and are doing everything they can, to get various organisations to believe that women's rights aren't important.
Strengthening the law and making it explicit that certain services MUST be single sex to protect vulnerable women or women in vulnerable situations would be extremely useful to avoid this deliberate blurring of lines in order to abuse the situation.
Doing things like making it a legal requirement to have single sex domestic abuse services available or single sex hospital accomodation or or single sex prison accomodation or single sex changing facilities for those who need them is making sure women are protected. This does not mean that services for trans people are removed. It means that provision of services for them (which will be covered by the EA as legally required) must take a different form.The entire point being that validation of identity does not take precidence over safeguarding.
This may extend to single sex toilet facilities in certain settings too. Arguably, this should definitely be the case in schools due to them being minors.
The exemption clause was always one about proportionality and was supposed to protect women. It is clear that it practice this clause is not having the desired and intended effect to provide that protection in law. Therefore 'tidying up' the law to reflect the original intention and the need to safeguard women, is not the 'gotcha' you seem determined to make out.
The entire point and problem is the degree to which males have riden roughshot over the exemption clause and made a point of demanding unlimited access without any consultation with women or ethnic/religious groups over the implications.
This clarification about the need to ensure women are adequately safeguarded in certain situations and there is a legal responsibility for organisations to do this, might make organisations take a different approach to planning and service provision. None of this takes away from trans people if done properly. It means that both should be protected by law and served properly, to ensure you aren't getting women self excluding and trans people without services.
I think this business about trans women 'just wanting to pee' and 'having a right to pee' needs to be held up for what its about - validation not concerns over safety. If its about just wanting to pee, then the sign on the door does not HAVE to be the ladies. It can be a mixed sex provision which is clearly marked. This means, both males and females can use it in line with their ideological beliefs, as self ID effectively makes all facilities mixed sex anyway.