Let's assume the calculation is correct and you actually earn back in 11-13 years. You are better off investing the money in something like the S&P 500 where you'd double your investment in about a decade without the hassle.
Things will start to get interesting where €1600 don't buy you 5kWh but double or triple the amount.
I can imagine most people are better off either investing like I said or in insulation.
But that makes you more dependent on externalities, a battery makes you more independent instead.
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€1500 can already get you 16.1kWh.
The investment point still stands, though you could argue both come with risk/reward, energy prices aren't guaranteed to be stable.