Stopping self id won't help with this.
But self-ID will make the problem worse.
The EA is linked with the GRA. There is stuff in there about the gender someone presents as being taken into account in the case of someone who doesn't have ID in their chosen gender. In the case of someone who has ID in their chosen gender, their appearance is no longer of any importance, since their legal sex is what is on their documents, and that is how they have to be treated.
An obvious male who has no ID which says he is female can be treated as a man, no matter how much he declares himself to be female. An obvious male with ID which says he is female has to be treated as female.
The way the GRA and the EA interact is what is important here. They don't stand alone with no relationship to each other. A GRA which says that any man can become legally female simply by signing a document renders all the sex-based protections in the EA meaningless.
If anyone is free to choose their own legal sex, what does 'sex' actually mean?