You're definitely right about that, but projecting the color space onto a cube and then seeing how it distorts everything has a certain visceral feel, like looking at the Mercator projection and seeing huge Greenland and tiny South America. You know all map projections are wrong, but the Mercator is wrong in a way that lays map projection distortion completely bare.

Without seeing the cube viz in my link, I'm likely to look at CIELAB and say, "oh, sure, but you can just take out the brightness and then it's all flat again." The cube makes it clear what happens when you do that.