I guess you could further insult me or provide your own napkin math.
Sure, let's say the summer months bump the Texas electric bill to $167/month (8$100 + 4$300). The previous model was assuming free electricity. My quick search is revealing that using differential pricing in Texas, the difference from the normal rate (~$.16) and the low rate (~$.08) saves ~$.08/kwh. Assuming you could perfectly offset all usage onto the cheap rate, that would yield a monthly savings of $83.5. Which yields a $10000/$83.5 = 120 month or 10 year payback period.
Then again, we forgot to right size the battery system. This site[0] claims an AC is going to use 16kwh/8 hours. A Tesla Powerwall is 13.5kwh. If you want the battery to fully cover your AC needs alone, you will need at least one additional battery system.
Naturally, we are missing out on maintenance, opportunity costs, grid connection fees, potential rebates, etc, but I think we have indeed landed on a more nuanced model.
[0] https://learnmetrics.com/how-much-electricity-kwh-do-air-con...