TheSporkforeatingkyriarchy - I think we agree though possibly wouldn't frame the argument in quite the same way. I would argue that children up until about the age of 7 have a wonderful fluidity of gender, as it is socially constructed, with boys and girls both being quite happy to play knight or princess, to dress in dresses or trousers, pink or green, to love all things sparkly and love pushing dolls in prams or play with train sets.
It's from about that age that the insidious messages that things are "for boys" and "for girls" start to be seriously absorbed, they start to be ridiculed by adults and their peers for liking the "wrong" things, that they find they have to slot into one box or the other with very little opportunity for overlap. And of course there is a huge number of children to whom this does a lot of damage. With those having the greatest dysphoria between their actual selves and society's expectations of them suffering the greatest damage.
So yes, I agree with you that the society needs a radical overhaul. But instead of making it easier (for want of a better word) for people to jump completely from one box to the other, what we need is a society where genitals are irrelevant to anything except the act of reproduction itself. It's not about being trans or cis, it's about being human in a society that would try to split us into two almost completely separate species.
This is the problem I have with the whole concept of trans - that for anyone to identify with the "wrong" gender, we need rigidly constructed definitions of what gender is in the first place in order for trans people to identify with them. You don't see transwomen wearing jeans, having short hair and not wearing makeup. Transpeople tend to fulfil every stereotype of the gender they identify with. What if there were no stereotypes? I truly believe the answer is to tear down gendered expectations of everything rather than to fight so hard to label people one way or the other. So much effort seems to be being put into accommodating trans people, to the extent that children are being given medication to delay puberty to make gender reassignment surgery easier, rather than any effort at all being put into making it okay for people to just be people, be that a person with a penis who likes to wear dresses, heels and makeup, a person with a vagina who likes to race motorbikes and drink beer, and every point on the spectrum inbetween.
Sorry, OP, I know this isn't what you asked. But the concept of gender dysphoria is a very complicated one and IMO needs examining from a societal viewpoint instead of lots of individual viewpoints.