These type of systems are incredibly popular right now in Germany. Supermarkets sell them quite cheaply as well.

I think it’s an interesting product but not likely to be cost effective in areas that have reliable power. It’s also not likely going to reduce emissions in areas with low to semi-low CO2 electricity production. I imagine their sales with either be to people who want more energy reliability or to people who are misguided in to thinking it will reduce emissions over there local power supply.

Particularly since the lifecycle emissions of distributed systems like this are inevitably higher than those of a centralized system (and more costly!)

To be honest, when I went solar 8-9 years ago, "environmental benefit" did not enter the equation, it was all about the cost I was paying for electricity.
I just recently purchased an ecoflow river, using it as an ups, and the cost to me was minimal, got it at dealers cost, again "environmental benefit" , didn't factor in.

They are a really good option for places without a good grid. Having some electricty makes your life so much better. You can already find solar panels in slums and nomads use them a lot. That makes sense. Other then that it is a decent way of adding a lot of solar panels to buildings, instead of large solar farms covering up valueable land. Having a decentralized grid has its advantages and being somewhat independend from the national grid also has its merits. However it is more expensive then solar farms and other large installations as economies of scale do not apply. Batteries in case of no or a bad grid are okay, but for a properly working grid they are just too small. However what makes sense is to use batteries you have at home anyway smartly. Charging your electric vehicle at the right time for example makes a lot of sense. In a way heat pumps and freezers heating up or cooling down more, when electricity is cheap is also a good idea. However purpose build electricity storage at home is wastefull, as just by it size a national grid will have much smother consumption and more different electricty source in more place to require significantly less storage. In theory it is always windy or sunny somewhere in the world, so a global grid, might not need much storage at all.

If you did the math I would strongly suspect this unit could never pay for itself. In that case you're either using it because having the backup power is worth it, or because you believe there's some environmental benefit. On the environmental front, again, I can't imagine it'll ever "pay" for itself. So... Well, ok, or you get it because solar power and batteries are fun.