The average content of gold and silver and of platinum-group metals is very similar in the whole Earth and in the rest of the bodies of the Solar System.
Nevertheless, in the crust that covers the surface of the Earth, the abundances of gold and silver and of platinum-group metals are many orders of magnitude lower than their average abundances in the Solar System.
For instance most of the silver has remained in deep parts of the mantle when the crust has formed, so silver is 11 times less abundant at the surface of the Earth than in the Solar System.
Gold and the platinum-group metals have gone to even higher depths, in the iron kernel. So at the surface gold is almost 300 times less abundant than in the Solar System, rhenium almost 600 times and nickel more than 900 times less abundant than in the Solar System, palladium around 3000 times, platinum and ruthenium around 5500 times and osmium and iridium around 50000 times less abundant than in the Solar System.
Similar numbers apply to all of the 8 planets that are big or medium-sized and also for some of the small planets and big satellites, because all these have been melted at some point in their history, when all the metals with high affinity to iron or sulfur have gone to inaccessible depths below the surface of those planets.
In the outer parts of the Solar System, the bodies are covered by thick layers of ice, but for the 4 inner planets the silicate crust that we see covering their surface is similar to the slag that forms at the surface of the iron smelted in an iron furnace and it is similarly depleted in the metals with low electropositivity.
You can also find asteroids that are enriched in platinum-group metals, by that same process. The shattered core of an ancient ("Iron catastrophe" differentiated) planet should be highly enriched in these metals.
16 Psyche might, or might not, be such an object. If so its surface is still covered by a "rubble pile" layer of rocky material.
You are right, but the enrichment of those asteroids in platinum-group metals is very small in comparison with the corresponding depletion of the surface of the planets.
While the depletion has reduced the amount of platinum-group metals by many thousands of times, the enrichment only increases their concentration a few times over the average concentration.
The reason is that the planet cores still include iron, one of the main 10 elements of the universe, the least abundant of which is many times more abundant than all the other elements combined.
The enrichment consists only in the removal of the magnesium, silicon and oxygen from the planet core, while the iron stays there.
Even with all the platinum-group elements in the core, their abundance cannot increase beyond the limit imposed by the ratios between their average abundances and that of iron (actually their abundances become a little larger than those ratios, because a bigger fraction of iron remains oxidized in the mantle than the corresponding fraction of platinum-group metals, but the difference above the average ratios remains very small).
Nevertheless, in the crust that covers the surface of the Earth, the abundances of gold and silver and of platinum-group metals are many orders of magnitude lower than their average abundances in the Solar System.
For instance most of the silver has remained in deep parts of the mantle when the crust has formed, so silver is 11 times less abundant at the surface of the Earth than in the Solar System.
Gold and the platinum-group metals have gone to even higher depths, in the iron kernel. So at the surface gold is almost 300 times less abundant than in the Solar System, rhenium almost 600 times and nickel more than 900 times less abundant than in the Solar System, palladium around 3000 times, platinum and ruthenium around 5500 times and osmium and iridium around 50000 times less abundant than in the Solar System.
Similar numbers apply to all of the 8 planets that are big or medium-sized and also for some of the small planets and big satellites, because all these have been melted at some point in their history, when all the metals with high affinity to iron or sulfur have gone to inaccessible depths below the surface of those planets.
In the outer parts of the Solar System, the bodies are covered by thick layers of ice, but for the 4 inner planets the silicate crust that we see covering their surface is similar to the slag that forms at the surface of the iron smelted in an iron furnace and it is similarly depleted in the metals with low electropositivity.