If this was really and truly just about documents then there would be a simple solution.
Make it so that anyone can change the sex on their short form birth certificate at a whim, as demanded by TRAs. Let people put whatever gender they want on it. I don't know what the purported reason is that trans people need official government documents that pretend they are the opposite sex, let alone why it's supposed to be a human right. But whatever.
And at the same time make sure no one can change the sex on their long form birth certificate. That way in situations where sex matters (hiring rape crisis workers, doing DBS checks, prison admissions, etc) there's still an official record of what sex someone is.
We all know that this compromise wouldn't be acceptable to TRAs because the actual goal here is to eliminate women-only spaces. But if it was just about documents and certificates this shouldn't be a problem. It's not like there are many occasions in your life when you actually need your long form birth certificate.