Why does the chromaticity diagram look like that?

It's probably good to start with XYZ, but we have much better colorspaces now that do a better job at correlating with our vision.

Mainly CIE 1976 L',u',v' and even more recently ICtCp from Dolby research.

CAM-16. When in doubt, ask the color scientists :)

The xyY colour space is designed such that the colours of light you get by blending two points all lie on the line between the two corresponding points. This makes it extremely helpful when you want to figure out which colours you can make with a particular set of primaries. Similarly you can draw the colours corresponding to pure wavelenghts and figure out the entire space of physically possible colours by taking its convex closure.

These features are not really replicable in any other colour space, at best you can use a linear transformation of it (which XYZ already is, and it has almost all properties you could want of a choice of basis).

Oklab is even better.

https://bottosson.github.io/posts/oklab/

That's true. And I will add that the viewable color gamut of a display can be depicted with a simple triangle on the xyY plot. All you need to know are the three chromaticity values for the reg, green and blue phosphors — they make up the three corners of the triangle.

No, it's not, by definition. It's one matrix multiplication to do an approximation of it. More here: https://news.ycombinator.com/item?id=41081832

The only claim to superiority it makes is gradients, and that's a category error: they blend polar opposite hues in the Cartesian space (i.e. x / y / z), rather than polar (i.e. h/s/l). Opposite hues mean lerp'ing in cartesian brings it through the center of the circle, 0 saturation. Thus, blue and yellow do combine to a off-white. Engineering around it indicates something fundamentally off, much less that it is better. I don't ascribe ill intent but I do worry very much about how widely this is misunderstood.

I don't think starting with XYZ and color matching functions is a good idea. LMS and cone response functions are a more fundamental and intuitive description of human color response, so if you're going to bother with XYZ at all, you should arrive there from first principles, via LMS.

And when you're done with XYZ, check out XYB used in JPEG XL and jpegli:

https://giannirosato.com/blog/post/jpegli-xyb/