The mapping is not one-to-one though - for example when S is 0, all values of H give the same resulting colour, and worse when V is zero both H and S are useles

The mapping is not one-to-one though - for example when S is 0, all values of H give the same resulting colour, and worse when V is zero both H and S are useless. So an image exploring the full HSV space should look different, probably with a lot more of the grayscale. I too have misgivings about HSV, the discontinuities created when generating hue ramps being particularly cruel. Using a rotation about the luma axis in YCbCr space gives much smoother rainbows but sadly not ones which hit all six primaries and secondaries. It's frustrating problem that perceptually H, S and V or L are what we think of when specifying a colour, but mapping them smoothly to RGB displays is so tough.