There can never be a diagnosis for identifying as a woman - it's a self-reported subjective mental state, so in the absence of veritaserum we're buggered on that one.
That doesn't mean we can't at least attempt to differentiate between males who seek to modify their bodies to alleviate psychological distress, and males who seek to violate the integrity of category woman for kicks. Neither should be in women's spaces, I agree, but the former have a medical condition that warrants accommodations (such as third spaces) whereas the latter group deserves branding with a whacking great D for Dickhead in the middle of the forehead so all women know who to avoid.
The GRC could theoretically be used to distinguish between these two subsets of males, if it's only possible to get one with intractable bodily dysmorphia, as used to be the case. Wouldn't be a perfect guarantee but would mean GRC holders as a class would present a statistically lower chance of sexually preying on women because this subset has historically been almost exclusively male-attracted.
At things currently stand, the ones with a medical diagnosis of a psychological disorder don't have any way of distancing themselves from the dickheads who are only in it to trample women's boundaries.
That said, no one gets a certificate of diagnosis to prove their legitimacy for any other medical condition (which as an aside makes life a lot harder for many people, myself included) - why are we singling out trans people / people with dysphoria for this special accommodation? I would pay a lot more than a hundred and forty quid to be able to get a certificate I could present to the assessor next time I'm hauled for an assessment instead of going through the demeaning rigmarole again.
Sorry, I may be rambling. Tl;dr you can filter by motivation, and there's merit in this even if no motivation is sufficient to access women's spaces.