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> the gamut "depth" is dependent on the component values (like lightness and chroma)

This is an unavoidable bug (feature?) of human vision and computer displays.

Using models like "HSL" or "HSV" is a way of trying to sweep it under the rug, but it doesn’t really work very well and ends up causing a lot more trouble.

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yah, visual perception isn't uniform in all directions, but i believe it's more that those distortions (the kinks and valleys) comes from trying to make the color space perceptually even to humans (and human perception has variation as well). however, there's no perfect way of doing this in all vector directions, so it's a multi-dimensional optimization problem that can only minimize distortions/maximize evenness, rather than provide a singular best analytical solution. as a result, the color space comes out like a spikey blob, to match our numerical color scales to human perception, since the opposite of coercing human perception onto uniform color scales is not feasible.

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