But what does gender reassignment actually mean?
I can't see that there is actually any practical difference between people with a GRC and people who just self ID as trans, since as you correctly point out, very few people actually have a GRC and even among those who do, it doesn't appear to be actually used for anything.
There does need to be a wider discussion about when or indeed whether it is appropriate for people to be allowed to use single sex spaces or compete in sports for members of the opposite sex.
My own personal view is that I do not have a gender identity, I do not define myself in terms of gender - which seems to be nothing more than regressive stereotypes - and so I do not consider that I share a gender identity or a gender with trans women or that their perception of themselves has anything to do with me or other women.
I'm struggling to think of even one situation where society actually distinguishes between men and women and where the relevant factor is "gender" rather than sex.
All of this is really just a belief system, designed to allow a small and self-selecting group of people to use spaces for members of the opposite sex, despite the fact that that defeats the purpose of that space being single sex in the first place, and despite the fact that the members of that group have not consented.