Would you like to explain that in more detail? So what do you mean by 5-6kWh from 4kWh storage? Is that per day, per week, per month? What does a period where "nothing" is generated mean? How large is your photovoltaic system?
5-6kWh is needed during the period when nothing is generated (so from evening until the sun shines on the modules again in the morning). The system is 6.5kWp small, oriented 45° exactly to the south (great in winter, about 9000kWh generated in one year!) The battery is therefore empty in the morning before electricity is generated again. My brother has on the other, slightly larger semi-detached house half, an 8.5kWp system with 8kWh battery, so we can compare well. For us, the question of "is it worth it" never even came up. It's just KfW40+ plus passive house. With so many subsidies (which no longer exist now), the battery was even worth it (which was also a condition for KfW40+).