I believe that there have always been some people with gender dysphoria/incongruence.
There have always been people unhappy with their bodies (nose too big, breasts too wonky, hair too curly or too straight or sparse, wrong number of legs). And there have always been people uncomfortable within the restrictions of rigidly divided, sexist societies. But that doesn’t mean anyone is 'really' a sex other than the one they were born, or that 'gender identity' is real. Every society with a 'traditional third gender' is rigidly controlling, deeply sexist and usually homophobic - and the gender allowance props up those systems (and not to the benefit of women). Better to reform the system so the safety valve isn't needed, rather than fiddling about trying to marginally improve the valve.
I have long argued for third spaces and revising the GRA and EA2010 to separate sex and gender identity.
I agree the EA needs to sort out the mess of using sex and gender interchangably. It doesn't currently contain anything about gender identity, and shouldn't (unless and until someone can pin down what it is and prove it actually exists). There's quite enough undefined in there without adding more.
The whole point of the GRA is to conflate sex and gender - you couldn't rewrite it to separate them in a way that would fulfil the purpose it was written for.
Third spaces are pointless if nobody actually wants to use them. At best they're a waste of time and effort. Usually they end up giving men even more than they already had by taking some of women's share - divide the prize pot, the room, the opportunity 3 ways instead of 2 and give men 2/3.