If grid storage batteries are economical in the general case then why wouldn't they be doubly so in a place where the inverters are a sunk cost and you're saving the transmission costs because the load is at the same site as the batteries?
The competition isn't the cost of generators, it's the cost of grid power, or the cost of operating gas generators every day.
They aren't economical in the general sense. They are economical to provide frequency stabilization, grid efficiency, and maybe a few hours of demand shifting. They're not yet economical to store solar power during the day and discharge it at night. We are getting closer but I don't think we are quite yet there.
As far as I can work out, the cost is competitive as long as you're using the capacity every day, especially when it lets you avoid paying transmission costs. The thing that doesn't work is to have enough battery storage to handle extended periods of low generation, because for that you need dramatically more storage capacity while only using the surplus on rare occasions. But a data center could use the grid or backup generators on those rare occasions while still using batteries overnight every night.
The competition isn't the cost of generators, it's the cost of grid power, or the cost of operating gas generators every day.