Your computation is off: it's 0.014 EUR/kWh, ten time less and far below kWh market prices about everyhere in the world.
As for cycling the industry standard is give the number of cycles to 80% capacity remaining so the battery is far from dead at 5000 cycles. The simple division I used is conservative.
No, it's not. From the link I posted (in Dutch unfortunately, I'll translate the relevant bit):
Small integrated battery:
3.5 kWh
Starting at about € 2.100,-
You yourself indicated in your post that integrated batteries (as in: the ones with battery management, that you can actually use to store energy in as opposed to a bunch of lose cells) are more expensive. They are more expensive indeed. I did the calculation. They boil down to 0,12 EUR / kWh in the example above.
The price of cells is not directly relevant, since you can't actually buy cells and just throw them at your house to magically start charging/discharging when you desire.
Well I bought cells a few years ago and use them with the necessary components, and those don't multiply the system price by ten.
BTW because I'm lazy to expand my system I just ordered 14 kWh of fully packaged LFP battery (box, BMS, cells, breaker) for $1800, $130/kWh, $0.026/kWh cycled.
As for cycling the industry standard is give the number of cycles to 80% capacity remaining so the battery is far from dead at 5000 cycles. The simple division I used is conservative.