You cannot use a centrifuge to separate solid iron.
Using a centrifuge with liquid iron would create a gradient of concentration of the heavier elements dissolved in it, but that would not be enough to separate them.
All that could be done with a centrifuge with liquid iron would be to obtain an iron alloy enriched in heavy elements. However, I doubt that it would be possible to make a centrifuge for liquid iron that would have a lifetime sufficient to process quantities of the order of one million tons of iron. I do not think that until now anyone has ever tried to make a centrifuge that could work with a liquid metal at such a temperature. Most materials lose their strength at such temperatures, so the risk of breakage for the centrifuge would be extremely high, a risk that is increased by how heavy iron is.
It is also not clear if such an enrichment of the heavy elements would bring a sufficient simplification to further processing steps to make it worthwhile.
Iron and platinum have different melting points. If you melt the alloy, then spin it to concentrate the platinum, couldn't you coax the platinum to separate out as solid clumps by adjusting the temperature?
Alternatively, there are differences in magnetic properties that could be exploited...
This isn't my field, so I'm just spitballing. I bet if you can get the cost of launch and interplanetary transit to be low enough for people to really start tinkering with asteroid mining though, someone will crack the metallurgy issues...
Different melting points are easy to exploit only when metals do not mix in liquid state.
Even when metals do not mix in solid state, but they mix in liquid state, that usually cannot be used for separation, because the liquid solution will become solid at a temperature different from the melting temperatures of the components and lower than them, and the solid alloy will consist of the component metals intimately mixed at the level of microscopic crystals, so you cannot separate them (this is called an eutectic alloy, like the lead-tin alloy used for soldering, where by solidifying it you do not obtain separate lead and tin, but just a non-separable alloy, and by remelting the solid alloy you obtain a liquid solution, where again, the metals cannot be separated).
If the metals also mix when solid, the solid metal is a solid solution that does not melt at any of the melting temperatures of its components, but at an intermediate temperature, and the metals cannot be separated regardless whether the alloy is solid or liquid.
Here, in asteroid cores, the precious metals are present in a very small proportion, so they form either a liquid solution when molten or a solid solution when solidified.
The melting temperatures of platinum et al. do not matter, the melting temperature of the alloy is slightly lower than that of iron, corresponding to that of an iron-nickel alloy. The other alloying elements are in quantities small enough that they have negligible influence on the melting temperature.
In conclusion, differences in melting points can only very seldom be exploited for metal separation and they cannot be used for the iron alloys of planetary or asteroid cores.
You can exploit only either the difference in boiling points or the differences in chemical reactivity with acids or oxidizing agents.
