Your $0.20/kWh is more likely to match reality.
My figures are bottoms up best case. But including my expectation it will go down in flames after 25% of claimed life, we arrive a exactly the same figure (well, not quite; you included inverter and PV.)
I expect PV to last 25 to 40 years (but some bad panels die young.)
Quality inverter to last 20 years.
Battery to last 16 years of 1 cycle/day (if 6000 cycles is to be believed).
My alternate way to determine cost is 10% of purchase price per year for long-lived assets. That bakes in some interest rate. So exactly what you did, except I apply it to things not expected to wear out.
Yes 10 cents per kWh for storing energy that cost 5 cents to produce with solar. If you were arbitraging the grid that cost would be higher plus in my case Non Bypassable Charges of 2.5 cents have to be added because I am on NEM 2.0.
And I've said 5 cents to store a kWh that cost 2.5 cents to produce (only if same inverter supports battery.)
I recently paid $2000 for 3x SBS 5.0, $3000 for 2x LG RESU-10H. Those batteries have about half the cycle life of LiFePO4, works out to $0.085/kWh if no other costs to install.
Marginally worth using to arbitrage my $0.20/kWh spread between on/off peak. If they served me for occasional backup, using for arbitrage would let them pay for themselves, backup is free. Except first night of a power failure would be spent in the dark, because they would be drained every evening when peak rates ended.
I was primarily interested in AC coupling them to SI + AGM, keeping AGM at float thereby extending life. Not sure they will respond to frequency shift for both charge and discharge. SMA denies "off-grid 60" applies to SBS, says that is an SB thing. I have a screenshot from their instructions indicating otherwise.