I feel the battery is so we can use an appliance without worrying that we will get heavy cloud cover before we have finished using it. And also so when the solar is only producing 1 kW we can use a 3 kW appliance and the solar for three hours can supply an appliance for one hour.
I started with 3.2 kW, and two problems, output limited to 3 kW and input limited to 2 kW, so was exporting when battery not fully charged and importing when two appliances took us over 3 kW. Yes, the battery did not last that long in the evening, around 9 pm was around the limit, but also being charged overnight, it would bridge the gap very well between 5 am and when the sun came out.
The second battery did help with 4 kW charge limit and 5 kW discharge limit (size of inverter) however it resulted in 2.88 kWh (90%) being used every night which was not needed, my rate was 8.95p per kWh so cost me 25p per day in the morning to have the extra capacity, but saved 90p each evening, so 64p a day saved at start/finish rates, but most the extra saving was during the day when not exceeding the 4-5 kW limit but was exceeding the 2-3 kW limit.
However, as summer came, and I went to a single rate tariff, I realised the pair of batteries were taking me nearly until the sun came out, this resulted is off-peak tariff costing me more than a single tariff. So starting on 5th this month I hit 10% with batteries and broke even with solar 3:30–8:30, 4:00–8:00, 5:45–9:30, 5:30–8:00, 6:30–8:30, 6:45–9:00, 8:30–9:30, 7:30–8:00, 6:15–8:30. These times very little used, so total import for whole day, 0.1 kWh to 2.3 kWh. And in that time, looking at recorded battery charged and discharged figures, around 1 kWh to 1.5 kWh more than the battery capacity, showing how much used to smooth out peaks and troughs.
If I go back before the 5th, then I have the charging off-peak, so warps the results. But taking whole of January this year
31 days, so daily average battery discharged 7.34 kWh and battery charged 8.2 kWh and 6.4 - 10% means batteries can only hold an useable 5.76 kWh. I see this

in my software, I know T1 is time it charges from off-peak, not sure of the rest, and this

which allows me to set things, but not really sure what they do, there has been a software update, and not sure how it now all works.
But the start/finish times of off-peak, with Flux, is a bit too late, (2 am) is winter will have run out far before then, I like most people use more power in the evening to the morning, so the Intelligent Octopus Go – EV Saver would be ideal for me, and I would get most solar panel and battery owners. But the "Intelligent" bit I read as giving Octopus control of when the battery in the EV is charged, and when I looked at export rates, they were well down on what is offered with Flux.
So it is a gamble even if you did have an EV. And locked in for a year, so need to consider winter as well. Same as how much to keep in reserve for power cuts, my batteries on a power cut stop discharging at 3% and with power 10% so 450 Wh held in reserve, so it would depend on the time of day we got a power cut, how long would my central heating and freezers run for? If power cut now, likely weeks, lighting and other electric use is not on backed up power, but at midnight, in winter, unlikely to last the night.
But the move to UPS for freezers also means two RCD's for freezer supplies, so less likely to trip due to RCD tripping as well. I hope I never need it, but seemed prudent to set it up anyway.