In a sense, yes. The true "freshness" of a color is shown on the color picker as the distance from the center of the circle. This is equivalent to the chroma component of CIELUV, the color space that HSLuv is based on. The problem with that component is that the maximum chroma is different for different hues, so if you were to move the hue slider while keeping true chroma static, you would run into impossible colors (such as dark saturated yellow).
This is a fundamental trade-off. If you need true saturation, you can use CIELUV and deal with impossible colors. If you need a color space that doesn't have gaps, use HSLuv and deal with a suboptimal saturation. The strongest claim I can make about HSLuv's usefulness is that it is a better HSL.
Hope that helps.
EDIT: You gave an idea that it would be useful to show another slider on the picker called "C", showing the chroma component with gaps.
> You gave an idea that it would be useful to show another slider on the picker called "C", showing the chroma component with gaps.
Yes, that would be nice. But as I understand it, fixing C would cause the H slider to show gaps too (?) Also, if you show sliders for H, S, L and C, then I think it would not be clear from the interface which sliders are fixed.
This is a fundamental trade-off. If you need true saturation, you can use CIELUV and deal with impossible colors. If you need a color space that doesn't have gaps, use HSLuv and deal with a suboptimal saturation. The strongest claim I can make about HSLuv's usefulness is that it is a better HSL.
Hope that helps.
EDIT: You gave an idea that it would be useful to show another slider on the picker called "C", showing the chroma component with gaps.