There still must be some input of energy. From what I understand, the Sabatier reaction is really only viable from an environmental perspective if it is powered by some other non-carbon energy, such as solar or wind.

And if you have that surplus clean energy, you should spend it powering things that would otherwise be powered with fossil fuels - not trying to offset someone else's emissions. Carbon removal only makes sense in a world where nobody is burning any fossil fuels, and we're trying to lower atmospheric carbon. Lower, not offset.

I accept the argument that offset schemes have difficult practical problems, but at least theoretically “offset” means “lower”. It just means that your application isn’t necessarily reducing carbon. And it kind of makes sense—for an airline to get carbon neutral it would require immense investment in electric flight and decades of research and then more decades of incremental rollout. Instead that money and effort could be spent helping reduce a lot more carbon elsewhere now (e.g., replacing coal power plants with equivalent solar power).

Depends on the cause of emissions. A few are not for purely energy but involved in some kind of chemical reaction. Concrete and Metal extraction are 2 examples. Having a way to offset is important in a cheap manner. Metal extraction esp is a prob as carbon reacts with several metal oxides and reduces it releasing heat. Since it generates heat and creates the final product, it prob more efficient then the alternative electrolysis route.

But yes offsetting CO2 produced due to energy is a waste.

Which would only make sense if you were trying to initiate the currently deferred glacial epoch.

Yes, to convert CO2 to CH4 you need to break the C-O bonds. This takes energy.

With this technology, assuming it can capture large amounts of carbon, couldn't some of it be converted to fuel for current use and some of it sequestered. It would certainly take longer to significantly reduce the amount of CO2 in the atmosphere, but should still do the job. Instead of introducing new CO2 into the atmosphere by burning newly extracted oil, we would be sequestering some and "recycling" some.