>Charcoal is pure carbon.

Not really. It still has some of those metals that end up as white oxides when you completely burn the charcoal, and it still has a decent amount of bound oxygen. The volatile compounds are mostly gone (with a bunch of the carbon) but all the trace metals are still there too. Some processes are able to remove some of them, with the goal being a result that retains as much carbon as possible, but burning even the best charcoal still results in non-carbon ash.

Coke (a slightly different process) has a notably higher carbon content, but even that isn't nearly close enough to "pure carbon" to be considered chemically pure carbon. It's better as a carbon source for steel and more expensive that charcoal as a heat source, but from what I can find, its still just shy of 90% carbon.