I did the calculation for another discussion yesterday. For larger battery systems you can get 10kWh for about 2.4kEUR and with that 240EUR/kWh the battery would amortise itself quite quickly (6 years, ignoring interest [0]). But the Balkonkraftwerk batteries are more 1.6kWh (+ 1000W panels) + transformer for 1kEUR. The solar generation changes the calculation a bit [1], but if I ignore that then we are at 625 EUR/kWh, which would at least double, maybe triple the payback period (and then ignoring interest becomes much more relevant).
However this is largely academic as for my calculation you'd need to use more than 20kWh per day (2 cycles @ 10kWh). The cheapest battery-only normal-outlet system I could find was 900 EUR (but the AC/DC transformer is already included) for 1.6kWh, so 562 EUR/kWh. I don't think I even use the 3 kWh/day for that system... And we are talking <100 EUR/year savings. In the end (residential) electricity is just not that expensive (in terms of household budget)
[0] With a dynamic price rate you could do two cycles per day (loading in the night and at midday with lack-of-demand-cheapness and solar-cheapness) on 250 days/year and a spread of 8ct/kWh (there is some variation, but that should be somewhat conservative) you can get 500 cycles/year and about 40EUR per battery-kWh installed. [1] In the calculations above I took a rough look at the pricing data in Germany https://www.energy-charts.info/charts/power/chart.htm?l=en&c... and picked numbers for reasonably simple calculations. With solar you would essentially do the Midday charging for "free" from the panels, increasing the price spread in the evening. One could also take time-of-use rates for the calculation, which (currently) typically offer a structure of -6ct, -6ct and +4ct at night, midday and evening (vs morning prices)