And if you run the numbers, the battery which can deliver 6.2kW is only about 1.5kwH in capacity. This matters because while discharging slowly is fine, to gain any economic benefit you need to be able to charge at essentially full power.

If you have 100kwh of batteries and only 6kw of AC connection then it would take 3 days of typical solar charging to get them to full capacity. And any kwh sitting there that you don't charge/discharge is costing you money for grid batteries - the economics still depend on being grid interactive.

The best demand signal in my local grid for example is exactly 1 hour wide. Which means s you get 4 15 minute intervals to basically try and dump power for the best price.