LFP cells prices for direct sale to consumer are about 70 EUR/kWh right now. With 5000 cycles that's 1.4 EUR cent per kWh cycled out of the battery, so it fully makes economical sense in all electricity markets.
Fully integrated consumer battery prices haven't (yet) followed the decline in cell price, probably because there's lot of demand for this kind of product.
The real number is likely still significantly higher than 0,12 EUR / kWh due to battery capacity (and charge discharge efficiency) going down due to wear over time.
It does look like when the price of integrated storage products goes down more, it could become interesting for countries who have had very expensive energy policies (Denmark, Germany, Netherlands etc).
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.
Fully integrated consumer battery prices haven't (yet) followed the decline in cell price, probably because there's lot of demand for this kind of product.