1) Gamete production. Did you trouble to read the article, which deals with precisely that? Most of all: we do NOT define sex by reproductive ABILITY. That is a strawman that I see repeatedly from those who want to push the "sex spectrum" idea - presumably because they think it's a gotcha. It's not.

We define sex by which of the two sorts of gametes the body is set up to try to produce. It might fail to produce them due to all sorts of reasons. Eg in a vasectomised man, the epididymis not being continuous; you wouldn't say such a person is not a man.

>> to support the idea of sex as a binary or sex as less binary/bimodal/a spectrum…there are very qualified and very well-respected biologists that make either case. >>

Please cite a well-respected biologist who thinks that sex in humans is not binary. (I'll cite one who does: Richard Dawkins. Over to you.)

>> “why have we come to make sex so central, culturally and socially>>

(I've cut off the "only defined and relevant to reproduction" bit, as that's not how sex is defined; however this is an important question.)

Why is sex so central? Because the accident of our evolution has also made men stronger and taller, on average; and because they produce the small gametes their evolutionary strategy (inseminate lots of mates, fight other men for that right) is very different from women, who on average are smaller and less strong and bear the children (be very picky about mates, cooperate with other women most of the time). Our societies are often recapitulating our evolutionary roles. It's only by maturing into societies that don't emphasise strength or height or other male characteristics that we get past making sex a central lynchpin of our societies. I think it's called "feminism", and I approve of it.