When was the last time you had to show your birth certificate to access a changing room or sports team? I dont even know where mine is frankly.
Is it that unfathomable that it might just make someone feel better about themselves?
It's often not required and taken on trust or appearances - BUT, if it comes down to it, it's always there as a final way of ultimately proving something and forcing somebody who, going on all appearances and circumstances, disagrees with you, to back down.
I agree that most of us probably don't know where our BCs are (although you can always get an official copy of it for a fee, if it's needed); but I would venture that those who have been allowed to retrospectively change their BC probably DO know where it is, and carry it around with them, to 'prove' what they got it changed for in the first place - in the same way that you always keep your passport to hand when abroad, but never give it a second thought when you're staying long-term in your own country. My sex was recorded at birth and I've never doubted or rejected it - nor has anybody ever suspected me of being the opposite sex - so why would I need quick access to a document to prove the obvious and undisputed?
It might make people feel better about themselves, but that is absolutely not the purpose of a BC, which is an official factual document. It might make you feel better if your BC said that you were born in Sydney or Malibu, but if you were actually born in Rhyl or Slough, you just have to live with that. Nobody is stopping you from later moving to Malibu - but you were still not born there.
Much more seriously, your parents may end up being perpetually abusive to you throughout your childhood, to the point that you, very understandably, end up hating them and having nothing more to do with them from the second that you turn 18. You may long for the day that you can finally go and spit on their graves; but you still cannot ever change your BC so that it says your lovely Aunt & Uncle were your biological parents instead of them.