But the gender boxes have nothing to do with the sexed body, which is why we don't need them. Can you give some examples of gender boxes which are directly connected to our sexed bodies? Is there any way that 'gender' can be expressed which requires either a male or female body? Because I can't think of anything which would fit this description. If something can only be done by someone with a male body or only by someone with a female body, it's not to do with gender, it's to do with sex.
That might be true if we were dogs, but we are people and so we have a culture. Culture reflects our experience, not just as individuals, but as a class. People here talk about getting mixed up about individual experience and class experience all the time and yet mix this up. Gender is not just, or even primarily, about what we expect from individuals. It exists at the level of the class of men and women, which means you can have both individuals who do not fit into the expectation while also having the expectation, and there is not a contradiction.
But I would point out first that you are not correct that gender only refers to arbitrary cultural ideas associated with sex anyway. Look at something like customs and regulations around sex segregated spaces. Those are not identical to sex, they are constructed sets of customs and values we associate with sex, and they could be entirely different. We could easily take the liberal individualist perspective and cut out such leaves, or maternity leaves, or differences in expectations for fitness tests, and so on.
You could consider something arbitrary though, like clothing style or hair style. In many places differences between male and female dress are fairly minor, and nothing to do with function. They exist because people have an awareness in, and a very strong interest in, the fact of our sexed bodies. Humans are artistic, we reflect our interest in the differences between the sexes through our clothing or our hair or even language or things like posture. But this doesn't work unless there s a shared language or cultural expression. This idea that somehow people will cease to care or notice if we get rid of these kinds of customary associations - does anyone really believe that? Or think that people would even go along with that? It would require as mush authoritarian discipline as the harshest and most prescriptive of gender norms.
The two other examples I already gave you are to my mind the best ones. If you have men spending time together, and women spending time together, as most radical feminists seem to think is important, that will create a cultural output, be it in terms of language, preferred experiences, associations, speech patterns, whatever. And we will associate certain things with the two sexes, like motherhood, and all its associations, probably the most primal association of womanhood even though not all women are mothers, because we all have a mother. For men there will be other associations. We will see these reflected in our language, in our allegories, in our heroes. They will shape our thinking, our values, our self-image.