No suffers don't think their bodies don't function. That's my point. That the "wrong brain" story doesn't match the actual situation.
As to "feel better living as the opposite sex" I do sympathise and in theory that sounds like it shouldn't be a problem, right? As long as when it matters, like anything that is supposed to be women only, like sports or prisons or women's officerships or woman-only networking events, the people who are only "living as" understand they are not included, it should be fine, right?
But these are the problems with that.
Firstly, that is not how the genderist movement has framed trans people's needs. The demand has been to accept that someone wanting to "live as" the opposite sex is proof that person truly is the opposite sex in a way that is unphysical and undefinable but nevertheless more fundamental than mere body sex, and therefore such people cannot morally be excluded from any provisions or protections based on sex.
Secondly, let's say the TRA demands and Stonewall Law are rolled back to the sort of compassionate compromise you envision. What happens when our GD sufferer hits one of those hard boundaries? Now they have to say "Ah, actually I'm not, in fact, a woman. I only live as one", maybe in front of people who didn't know. That's going to be incredibly triggering for them. And of course those people should be accepting and compassionate, but there's still going to be a sense of betrayal or distrust that this friend has through lies or ommission mislead them about something so fundamental. And when I say it's fundamental, it's not the arrangement of the body itself so much as the difference in life experience and opportunities, the shared frustrations and common bonds that will have been assumed. No one likes to feel like they have been fooled. Knowing the person you thought you knew and could trust has been misrepresenting themself means knowing they held themself always a little bit back behind a character they were playing. It's setting trans people up for pain and rejection.
Thirdly, it places the friends who do know in the uncomfortable position of having to support the deception. Imagine you had a friend who wanted everyone to believe they were French. Seems harmless enough, right? But wouldn't you feel a little embarrassed knowing their French accent was put on? Knowing their memories of maman's crepes never happened? Wouldn't you feel a little uncomfortable introducing them to an actual French friend? Not because their desire to be seen as French is anything perverse or malicious but because they are nevertheless deceiving people and because they are living by stereotypes of something they have never truly experienced.
I believe the better path is to create more space in society for "feminine" (which should be renamed to remove it from female) personalities, preferences, desires and interests in men and "masculine" (same point) personalities, preferences, desires and interests in women so there is less genderised difference between the sexes for GD to arise in the first place.
And in that world, those men who still claim their GD means they need to be in women's private spaces, well their motives are pretty clear.