As far as I can see, the main argument for self-ID (over the current system) is that expecting people to get two psychiatrists to sign off on their application for a GRC is gatekeeping.
But it strikes me that there are lots of places where we have, and expect to have, gatekeeping.
I can't just waltz into the post office and get a passport over the counter. I have to supply my birth certificate (or previous passport) and get someone to countersign the application to say that I am really me.
I can't just put my children into any school I want - I have to apply through the local authority's website, and they reserve the right to check that I live where I say I live.
I can't just collect earnings cash-in-hand (well, I can, but it's illegal) - I have to declare those earnings to the inland revenue. I'm issued with an official NI number in order to do this.
Pretty much anything which gives some official legal rights and obligations to an individual involves gatekeeping. Why should "getting one's gender reassigned" be any different?
If we accept that the whole point of a "sex change" is to gain (with, at present, certain limitations) the legal right to be treated as the opposite sex to one's birth sex in most situations, then why shouldn't it be subject to gatekeeping? And if you don't fancy the gatekeeping, well, the brilliant thing is we live in a remarkably tolerant country where dressing how you want and asking to be called whatever you want is perfectly legal (though you won't get the official paperwork that way - but then, I wouldn't get a passport that way either).