So, the only rationale behind this seems to be that having the lived gender of the person on all documents will help in one specific case: preventing the person from being "outed" as their birth sex.
The way I've heard this is mostly for Drivers' license situations. For example, if we have a trans man who has been on T for 20 years, bearded, fully passes as a man, etc. In that case it might be a risk if in a strange bar they use an ID saying "F" - if the bartender / patrons are really violent transphobes, they could be assaulted. I see the point. If you do pass then that incongruity could potentially trigger a transphobic attack.
I would argue though that it's not much help to the vast majority of trans people who do not pass at all. For example, a non-passing but presenting as female trans woman whose ID says "F" goes to the same bar. The transphobe bartender will look at that ID, look at the obviously male person in front of them, call it for the fiction it is, and assault them anyway. Again the incongruity is only likely to make them angrier, not mollify them.
As for nonbinary, the transphobe is going to be like... Why does this girl with blue hair have an ID with "X" on it?
And for this legal fiction that benefits only a tiny proportion of trans people in a narrow range of circumstances (and none of them, except for perhaps the Passport office will ever need to see the birth cert by the way), and may in fact increase risk for the majority of trans identified individuals, we sacrifice the following:
The ability to accurately assess the impact of sex on crime rates, income, academic achievement, and myriad other public statistics.
The ability to use sex as a protected or considered characteristic for things like scholarships or awards.
The ability to name women's bodily issues with approachable language that any women can understand.
The ability to maintain even the option of sex specificity in those cases that the vast majority of people would agree are appropriate such as sport, battered women's shelters, reproductive care, prisons, and open-design changing facilities.