Is the Earth's core extra Iron/Radioactive rich?

The story is a planetoid the size of Mars struck the Earth in its early formation- the debris cast off in the impact forming our Moon. A little under spoken side benefit of this impact is that the Earth gained two planets worth of accumulated Iron and Radioactive core-materials... correct?

So we have an Earth today with a vigorous active Core, with no signs of cooling down or stopping any time soon. The heat is generated mostly by our healthy abundance of radioactives in our core. Our Geology is active, our magnetosphere protects our atmosphere, and the Carbon Cycle of life gets renewed with plate subduction and volcanic release (the carbon trapped in living organism remains in the seafloor eventually get subducted, melted in the mantle, and then released as Carbon Dioxide from volcanoes- keeping the Carbon atoms liberated from the remains and recycled). Without the active Core, Our planet would be cold, its atmosphere stripped away, and all life stopped because there was no more Carbon to build Carbon based lifeforms with- it ran out billions of years ago.

In short, we would be a lot like Mars. The Core of Mars has cooled and solidified. Its atmosphere stripped away by the solar wind, and its now a dead vacuum world. Is this the normal fate of a planet if left to whatever inner core composition it was able to accumulate during planetary formation? Is it simply not enough to keep geology going? Does a planet need to have an "extra serving" just to remain active?

So that is my question: IS the Earth a "double serving" of core materials- due to that fortunate impact? Does this mean that non impact planets in other Earth habitable zones would not stay geologically active without such a fortunate impact? Does this make a life bearing planet such as ours much, much more rare than we may think- as it REQUIRES such an impact of just the right size to barely NOT obliterate the planet to give its core the materials needed to run in perpetuity (well, for the life of the star, at least)... OR am I overstating the importance of all this?

So yeah, I was just wondering if we took into account the extra help the Earth got with that impact... or if we just take it for granted that other planets can retain active cores like ours pretty much indefinitely... when it seems other planets in our own system have all cooled down by now.