FWS covered quite a lot more than Schedule 3 part 7 (service providers) as you very well know. Otherwise, I find myself in agreement with you for once, somewhat to my astonishment.
Media can use whatever names and pronouns they wish. Using cross-sex names and pronouns can undermine understanding, though, particularly since a) people sometimes 'detransition' (like the male victim in the headlined story, and b) when snippets of news stories are quoted, some information gets lost.
Nor do I agree with @Merrymouse about editorial flexibility, which could also undermine understanding overall, and in any case only ever gets used in practice to try to portray trans people in the best possible light.
My preference would be eg:
TW charged with crime X: Rosie, who is a TW (previously known as Dave, he was born male, but now claims to have a female gender identity) was arrested, etc, etc (he/him throughout)....
or (less preferred)
TW charged with crime X: Rosie charged with crime X. Rosie is a TW (previously known as Dave, he was born male, but now claims to have a female gender identity) and we will follow the social convention of using 'she/her' pronouns for him throughout this report. Rosie was arrested, etc, etc (she/her throughout, bonus points for juxtaposing them with the word 'penis' as often as possible)....
But, pick a lane. Don't flip-flop.