Not compared to doing pretty much anything else with that power. Which includes easy things like pumping water uphill, charging lithium batteries, or just making H2 and distributing that into the gas grid directly.

To make CH4 from CO2 takes 8 electrons at (near enough) 2V, giving 1 / (96450 * 8) moles CH4 per amp second. Per tonne, that works out to roughly 1000$/tonne CH4 or 2900$/tonne CO2. Assm 4c/kwh.

So with an exceptionally efficient process requiring negligible capital expense or labor it is possible to convert 3000$ and one tonne of CO2 into 200$ of natural gas. Short of making rocket fuel on Mars, I'm not smelling even the slightest whiff of an application: which is why I am so derisive of the article's proposal - charitably it is at best proposing the equivalent of solar roadways.

Hydrogen is a lot harder to store than Methane, and afaik you can't substitute 100% Hydrogen for natural gas without changing large chunks of the heating infrastructure. But you're of course right that making hydrogen has a much better efficiency.

Britain is/was looking into just that with some moderate seriousness[0]; a quick google suggests as much as 30% enrichment. Though as I recall they wanted to use SMR/ATR on natural gas and bury the resulting CO2 in the north sea as opposed to electrolysis.

[0] https://www.sciencedaily.com/releases/2018/06/180611133412.h...