Except maybe nuclear, no source of energy creates new carbon. The question, vis-a-vis carbon neutrality, is "over relevant time scales, does this leave more carbon in the atmosphere (as opposed to sequestered in oil, coal, trees, whatever)?" If you create coal and then burn it, that's carbon neutral (modulo whatever you produced creating the coal). If you dig ancient coal out of the ground and burn it, that's not carbon neutral.
Right, there was no coal when the earth formed. It's all former biomass and was part of the biosphere. So we need to burn it to actually be carbon neutral. I did offer a refutation of this...
Yes, of course the coal hasn't existed forever, and before that the carbon was presumably part of the atmosphere. But that wasn't an atmosphere ever breathed by Homo Sapiens. We don't want to make sure the atmosphere matches that at earth's creation (it wasn't always even significantly oxygenated! and if we want to put back all the carbon that includes killing all life). We want to be sure our activity doesn't leave us with significant negative consequences.
It took 50-100 years for the glaciers to form. Global warming caused measurable disruption of the same ocean currents in 2016 and 2017.
So, replicating pre-ice age conditions, as you suggest we should, could easily lead to the collapse of most European states, and at least the northern half of the US.
If the term "carbon neutral" referred to all carbon on earth, then yes, burning coal would be carbon neutral. But that isn't what the term means.
Your idea is refuted by definition, not by science.
The same holds for the methane that's starting to be released as the permafrost in the arctic thaws. That used to be active in the biosphere, so why should it be a problem?
1) Coal; coal is a case of carbon sequestration. Coal was largely formed in the Carboniferous period, at this point plants had evolved to form wood which uses lignin in its structure. This allowed forests to form, but until the end of the Carboniferous fungi that could degrade and decay lignin were no widespread. This led to a bloom of oxygen in the atmosphere and a crash in carbon dioxide. The earth cooled and there was a mass extinction. Lignin decaying fungi then became widespread releasing the non sequestered carbon (that which hadn't formed into deep deposits of coal) from the lignin. In the carboniferous period the carbon from many 100's of millions of years of volcanic activity was sequestered by plants in coal deposits, since then the ecosystem has faced the need to absorb a smaller amount of carbon from just 300 m years of the volcanic history of the earth. This has resulted in the chemical balance of the atmosphere and oceans we have today, including the way that they interact with geology.
2) Methane in permafrost; I think that this is a much smaller amount of carbon, but the problem is that the iceage processes that have formed these deposits have resulted in a store of methane, rather than CO2, and methane is a very strong greenhouse gas. Injecting a large amount of methane suddenly could lead to a sharp period of warming.
Before coal formed the chemistry of earths oceans and atmosphere was different; there was sulphur in the water column of the oceans. Carbon dioxide was ~8 times the current level. The world was 6' C warmer, and at that time Sol was ~5% dimmer. Sea level was ~170m higher than now, and the seas would have been very acid - due to the carbonic ions.
Going back to a world like that wouldn't be a problem, for some bacteria, for animals with shells or bones, well - not so good. In fact, there probably wouldn't be any because the acid in the ecosystem would prevent calcification - rubber for bones! Expect worms, leeches, jellyfish and insects to profit.
This time round there will be no carboniferous swamps - fungi have the trick of decaying wood now, so the time of large animals on earth will be done, back to the Precambrian, but hotter, polluted (for a million years at least) and radioactive (for a bit longer).
The permafrost past/future is probably more benign; 70 -100m of sea level rise, some acidification - but nothing like enough for the end of skeletons. I think it would likely see a massive reduction of human population, but I doubt that humans or human technology would disappear.