In a vacuum I think that would be the natural conclusion, but IMO there's probably better uses for that energy (eg.: desalination plants).

Although I could totally see this being the case for CO2 + ... -> CH4 + ...

We can just directly convert green energy into hydrogen. For a lot of cases that is already more than good enough. Synthetic fuels may be needed, but possibly only in specific situations.

Yes and: H2, ammonia, methane, direct carbon capture, heat. Probably a few more.

Being a long time climate fatalist, I'm now guardedly optimistic about our eminent surplus energy future. If we can somehow keep warming to 1.5, we just might squeak thru this.