Are AA/AAA’s ever better than wired devices?

I currently rent and am not off the grid, but I figure this is a good place to go with this question. I’ve seen comments, even by off-griders, that approve of using AA/AAA-powered devices rather than wired devices. (Is “wired” the term for devices plugged in to an off-grid system?) Anyway, I don’t understand how this would be preferable. It seems that if a home uses solar power, it would be preferable to plug into the solar power rather than use AA/AAA batteries, even if the batteries are rechargables and one uses a solar-powered recharger. It seems like the batteries themselves would be a pointless waste, when there’s already a clean power source available. Even rechargable batteries have to be disposed of eventually. What am I missing?