Your calculation on AGM batteries is false, AFAIK.
AGMs (basically lead acid batteries) have a much lower lifetime (about 300 cycles, not 5'000 [1]) versus LifePo4 (Lithium iron phosphate, ~2'000 cycles [1]), to the point where it doesn't make economical sense to buy an AGM today [1].
As an example, you could get six 12.8V, 200 Ah LifePo4 incl. BMS from a US supplier for 3'5000 USD [2]. That will give you 15kWh (not w) of storage, so, more than the 'Powerwall' you cite and much more than your AGM batteries.
Your calculation has another mistake, I think. With AGM batterie, you can only use 50% of the labeled energy [2], so your calculation is off by another factor of two. With LifePo4 you can use about 80% of the labeled capacity, if you want to get a long lifetime out of your LifePo4 battery.
From another Source [1]:
[LifePo4] Up to 6 time the cycle life
AGM Deep cycle – 300 cycles @ 100% DoD
LiFePO4 – 2'000 cycles @ 100% DoD
Benefits:
Lower total cost of ownership (cost per kWh much lower over life of battery for LiFePO4)
Reduction in replacement costs – replace the AGM up to 6 times before the LiFePO4 needs replacing
I have Trojan AGMs that are well over 20 years old in my Golf Cart. They've had well over 2,000 charges and are still pushing nearly 90% capacity. No swelling, no leakage, nothing.
My grandfather's old flood-chargeable lead-acid golf cart batteries were double that age, or more, and had an easy 10K deep cycles on them when he passed. That cart went two rounds of 18 holes, plus fishing at the water traps afterwards, daily. He would change the fluid in them monthly.
Typical unsealed lead acid batteries can be maintained to last a long time. We used those to power an old warehouse with a solar array for a natural living commune in Memphis for over a decade. I can't tell you exactly how long they lasted as I had moved away from there while after that tenth year. Now once the plates have totally sulfated over, yes you aren't getting power unless you strip the sulfates away to reveal the plates again, but until then, acid refreshes work just fine, and you're looking at about 15 years before needing to replace the batteries due to sulfur coating if you only bother doing acid refreshes. You can get far longer if you know how to remove the sulfur off the lead plates.
The days of sub-1000 cycle deep-cycle lead-acid batteries have long gone. All it takes is knowing how to maintain them. Nobody seems to do that any longer. Most of these were made with maintenance cycles in mind. (Not AGMs, obviously, they're totally-sealed.)
AGMs (basically lead acid batteries) have a much lower lifetime (about 300 cycles, not 5'000 [1]) versus LifePo4 (Lithium iron phosphate, ~2'000 cycles [1]), to the point where it doesn't make economical sense to buy an AGM today [1].
As an example, you could get six 12.8V, 200 Ah LifePo4 incl. BMS from a US supplier for 3'5000 USD [2]. That will give you 15kWh (not w) of storage, so, more than the 'Powerwall' you cite and much more than your AGM batteries.
Your calculation has another mistake, I think. With AGM batterie, you can only use 50% of the labeled energy [2], so your calculation is off by another factor of two. With LifePo4 you can use about 80% of the labeled capacity, if you want to get a long lifetime out of your LifePo4 battery.
From another Source [1]: [LifePo4] Up to 6 time the cycle life
AGM Deep cycle – 300 cycles @ 100% DoD
LiFePO4 – 2'000 cycles @ 100% DoD
Benefits:
Lower total cost of ownership (cost per kWh much lower over life of battery for LiFePO4) Reduction in replacement costs – replace the AGM up to 6 times before the LiFePO4 needs replacing
[1] https://www.sealedperformance.com.au/faq/what-are-some-diffe...
[2] https://ipowerqueen.com/collections/12-8v-series/products/12...
[3] https://www.crownbattery.com/news/agm-vs-flooded-batteries-w....
(edited for formatting and typos)