You don't need a GRC to change the sex marker on your ID. Both DVLA and the passport office let you self ID anyway. So it doesn't change the first pass of checking.
But if an organization thinks you are a different sex to the one you purport to be and tries to check, the existence of falsified birth certificates means that organizations will find it hard to do that administratively. And it doesn't really matter how many there are, if you know there are false ones out there that the men who might be trying to access women's spaces are likely to have, you can't rely on any of them if the person you are suspicious of looks different to their purported sex. The fewer GRCs there are, the less often an organization will need to dig deeper, but they will still have difficulty doing things administratively - especially with Trans-identified people of the correct sex who look like they might not be of that sex.
The only reliable way will be a DNA check (as sports are only too aware).