Right. My point is that, as with a battery, you'd need to store the product so you can reverse the reaction. Practically none of our current infrastructure for using CH4 is set up to store the output CO2 + H20; it just dumps it into the atmosphere.

If you want to reuse existing CH4 distribution pipelines, that's fine, but now you need to pipe back the CO2 to the plant that makes the CH4 in order to complete the cycle. That's much harder than pumping CH4 and would require a whole new parallel pipeline infrastructure that can transport highly pressurized CO2 back to the source plant. Alternatively, you could regenerate the CH4 on location, but then you need to pipe the energy in; in that case, you're not using CH4 to deliver energy at all.

You could make the CH4 from CO2 in coal or something, but then you're no longer carbon neutral (since that CO2 will end up in the atmosphere rather than the battery). You could also try carbon capture, but honestly thermodynamics suggests that that will never be a viable solution; far easier to order your coffee black than to unmix the cream from it.

My point is that, unless I'm misunderstanding something, existing distribution systems for natural gas are not useful for CH4-based battery storage.