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.