What is it about their design that make these the ultimate place to put a pair of Kans?
Like I say, nothing specific. If Linn had designed the speakers using a solid stand they might have voiced them to suit.
They have a very wide base for the size of the stand masking them very rigid with spikes top and bottom. They are heavy enough to be stable without having so much mass that they either store too much energy or over-damp the speakers. Lots of open-frame stands of the day were almost exactly the same. Linn just made ones the right size for the Kans. Or got someone else to make them rather.