You can also use the better-implemented color picker for the HSLuv color space at http://www.hsluv.org/. HSLuv is just like LCH except that it stretches the saturated colors for each hue so that any saturation coordinate represents a valid color, unlike LCH’s chroma coordinate. The downside is that the color’s chroma (colorfulness) can change when you drag the hue slider.
To be clear, HSLuv, is based on CIELCHuv, the cylindrical transformation of CIELUV [0]; the LCH in David Johnstone's colour picker is CIELCHab, the cylindrical transformation of CIELAB [1].
Of course, that doesn't contradict your comment about the pros and cons of HSLuv's "saturation" component.