As stated above....
I really cannot think of a good reason, on my own, why this should be so....
Is it a mystery to geologists?
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Once you're in the metallic part of the Earth, the compositions of the different constituents (solid and liquid) are not determined by density.
The whole metallic part (core) is denser the the silicate rock part (mantle) which is why it is the core.
The concentrations of various elements in the solid vs the liquid are determined by thermodynamics and equilibrium partitioning. In a very simple sense, if you melt an iron-nickel alloy, it doesn't all melt at once. It melts continuously over an increasing temperature range, with coexisting liquid and solid. The solid will always have a bit more iron, and the liquid always a bit more nickel, until it is all liquid.
The core is a bit more complicated than that, but the general principle still holds.
When they are molten these metals dissolve within each other - ie they are in solution. Convection and diffusion will disperse and mix them; convection and accompanying turbulence mixes them at large scale and diffusion causes migration from high concentrations to low at small scale. Near a planet's core the gravity gradient is going to be limited, ie separation due to differential density is not a strong phenomena and the inner core itself is believed to be solid; there is mixing within the fluid outer core but no ongoing convection or mixing with or within the inner core.
The inner core would have higher iron content due to ongoing radioactive decay and lack of ongoing mixing, ie it is the oldest and given enough time the other metals in it including nickel transmute through natural radioactive decay - Nickel-56 beta-decays to Iron-56 (via cobalt-56) - with iron being the stable end product. Over time there will be less nickel and more iron.
(Note - I suspect that solid crystals don't form in molten nickel-iron until temperatures where viscosity impedes sedimentation and the crystals will be mostly taenite and kamacite - ie nickel-iron - rather than crystals of iron separate from crystals of nickel.)