Time-shifting. If you have a good way of storing it you could generate methane during the months when you have surplus solar power and use it in winter after you've depleted your batteries and the sun is not bright enough.

Probably (over) insulating the house is the most efficient way of minimizing energy loss. But then does an over-insulated house get overly warm in summer or easier to cool?

The air-sourced methane could be used for things that are hard to electrify/de-carbonify, and could reduce the use of ground based sources.

I'm wondering at what level of carbon tax it makes more sense to extract the carbon from the air to turn it into plastic than to use ground-based oil.