As for charcoal in a barrel, the only reason it's there at all is because there's no other way of producing the 'Red Layer' (caramelized oak) which gives spirits their characteristic colour (and a little sweetness). Sure, you can toast wood in an oven, but that does not produce a red layer. So you have to flame it, which produces charcoal as a byproduct.
And what the hell would distilleries or coopers do with mountains of charcoal if they did remove it? It's not strictly needed, just the red layer as I said before.
It was worked out centuries ago that the charcoal had no bad effects on newmake spirit, rather the contrary. It actually gave spirits a 'smoky' aftertaste, and more modern technology has proved it to be a reasonable filter of some of the harsher tails, though not near as good as dedicated manufactured filter carbons. So we have charcoal in our barrels, and everybody points to that and says "There's the proof that charcoal/carbon is necessary". Hogwash!
When barrels are refurbished, the first thing they do is scrape all the remaining charcoal out, to expose new wood. Then they refire them to produce another red layer. It should be obvious from this that there's only a limited number of times a barrel can be renewed, before there's not enough wood left to make a red layer, and still remain strong enough to withstand the strain of the contents weight. And the byproduct charcoal? It goes on providing its minimal filtering and smoky overtones.
To show how effective (or not) barrel charcoal is as a filter, try this...
Get 2 jars, half-fill each with storebought bourbon. Put a handful of fresh charcoal in one, and a handful of filter grade carbon in the other. Leave them sit for several days/weeks, then check the colour. I'll guarantee you the carbon jar has lost considerably more colour than the charcoal jar. But I'll also guarantee the charcoal jar is now a smoother, smokier bourbon than the carbon jar.
Hopefully this will put an end to the urban myth that charcoal/carbon MUST be used in spirits production. Clearly it is not. As THM said, make good likker to start with.