Problem with this idea is batteries on grid scale are always cheaper per MWh, so grid scale battery operators will eat away any arbitrage you could earn with more expensive consumer gear.
While the power doesn't go out often, it is a big deal when it happens and so a backup is useful. I'm still fixing the damage from the last one - the sump pumps not running for an hour in a rain storm is expensive. Fortunately it wasn't a long outage, much longer and the fridge/freezer would be a problem. In cold weather the furnace is important to keep running. There are other essential things as well that my house cannot survive without. Beyond that I want my computers to keep running if possible.
My sump pump hadn't run at all to my knowledge (I hear it so I think I'd know but maybe I was always gone or sleeping) for several years, but the power went out in a big rain storm and so the one time I needed it, it didn't run. (my old generator didn't kick on like it is supposed to, but I'm not sure if that circuit is wired to the generator anyway)
My electricity supplier sends me a message nearly every week saying if I use less electricity during peak demand times then I get free power at weekends. https://octopus.energy/saving-sessions/