I've thought about this a lot recently, because my mom keeps apologizing for "making me this way." She's worried about the opposite of what you're thinking, though -- that she made me trans by failing to appropriately cement a female identity as a child.
I was raised in a remarkably gender neutral house, the oldest daughter in a family of liberals and feminists. There were essentially no gender restrictions placed on me, and pre-puberty, my life was indistinguishable from that of a boy's my age. (With one exception: while I was free to shuck femininity, my identity as Female was rooted early and reinforced regularly. My earliest memory is receiving a CD-ROM titled "You Can Be A Woman Engineer" and my life was full of "anything boys can do, you can do too." So, while gender roles were non-existent, gender was very much still present, albeit in an abstract way.)
I think this masked my dysphoria for a long time, and allowed me to have a relatively free and happy childhood, but I don't believe it solves the problem or removes the trauma altogether. It actually raised its own, sort of weird, complication: I grew up with the understanding that Girl could be anything, I could be anything, and therefore whatever I was was automatically Girl. Great, as a cis person. As a lil trans kid, it meant that I voraciously devoured stories about girls who tricked people into thinking they were boys, selflessly disguised themselves to go to war/work, etc. I really took refuge in "girl becomes boy" stories, but when the euphoria of identification had passed, I would feel incredibly guilty. Here were these stories of women who were FORCED to present as men because of sexism and oppression. And then here was I, exploiting it, like some kind of gender traitor.
So, I don't know. I think that for a lot of trans people, gender abolition would relieve a lot of issues. It wouldn't erase physical dysphoria, of course, but at least some of the social aspects would be gone.
The only thing that makes me pause is a recent conversation I had with a disabled friend of mine. She is cis, but her experience with gender is almost more like a trans person's. She had to discover herself as a cis woman as an adult and basically reevaluate her whole identity and line of thinking, because her developmental disability so entirely overwrote her personhood, and more specifically, her womanhood. Society aggressively de-gendered her, to the point where she believed that [Woman] and [Disabled] were incompatible boxes. She was Disabled Thing, and the idea that she would experience life as a woman, with female desires and a female sense of self, was incomprehensible to those around her. It wasn't a malicious act, simply a product of ableism and society, but it makes me worry that, in a genderless world, people like her would fall through the cracks and become "the new trans," so to speak.
