If only we could use that extra power to make methane for later power plant useage
The obstacle for this process (and in synthetic hydrocarbon fuels more generally) is obtaining the carbon dioxide efficiently. Atmospheric carbon dioxide is in too low of a concentration to be viable. You could source the carbon from coal, but that makes it no longer carbon neutral.
Prometheus fuels is one of several startups pursuing this kind of technology. But it's still blocked on effective air capture of carbon dioxide.