I think the benefits of HUSL are kind of explained backwards, with technical details first and practical applications later. But once I saw their comparison of contrast (60% brightness random colors HUSL vs HSL) and the demo, it's pretty clear that HSL is way more difficult to depend on for random colors due to wildly varying contrasts.

Comparison: http://www.husl-colors.org/#comparison Demo: http://www.husl-colors.org/syntax/#506055

I'd be interested in seeing a version of the demo with HSL, for comparison.

I see. I guess I didn't really see much of a use case for random colors with constant variation of contrast. The demo does a pretty good job of demonstrating a compelling use case though.

The examples on the page are all at the same lightness, so you only see a slice of possible colors. The main point it's trying to show is that HSL's notion of lightness is rather useless. When it's trying to generate some background colors (with a fixed lightness of 60%), note that some of the HSL colors are much brighter than others, to the point that the white text becomes hard to read. By contrast, all of the HUSL colors at 60% are suitable for use as a background under white text. You can press the test buttons again to see more examples.

Those vibrant colors are not gone from the HUSL palette, they are there at the top. But they are not the only colors. There is more variation. The HSL palette is "over saturated" with saturated colors.