We did this many years ago for remote First Nations sites with an energy monitoring startup I worked for - saving them enormous sums of money (and carbon!) in the process. It's actually quite amazing how low some of the low hanging fruit is once you start looking.
That is really cool, our use case was powering an off-grid festival in a remote location. Our battery fit in a semi-truck (so it was fairly big, but not grid-scale). I don't remember the exact savings on fuel but it was ridiculous, like truly non-sense why doesn't everyone do it like that. I think the generator was on only about 40% of the time.
Even as backup power it still makes sense to have a battery attached because it extends the capacity of the system so much. The main problem is that you need some BMS software to coordinate the generator and the battery, but there aren't self contained solutions like this widely available (at least last I worked with it).