I don’t think the math works very well unless homebuilders start including solar in new builds.
1. Tesla batteries are like anything else with the Tesla brand name: Too Expensive Still Liberals Adore. My 5.14kWh batteries are $1,500 each with 19-year warranties guaranteed to slowly degrade and still be storing 50% as well in the final year. Why? Because they're not Tesla.
2. My system cost $33K with 32 panels putting out 10kW and storing 30kWh in battery storage. It'll pay for itself on about the 10th year (I'm actually in the middle of expanding it and I got an EV, but I'll go with the numbers as though I'm using just the original system because that's more practical than the uber large system I'm expanding it to.) That $33K is before the 26% tax credit. Last year it produced 58.5% of all the power I consumed in my two-story now all-electric house even with all the A/C I run in Alabama.
3. My 10-year pay itself calculation isn't based at all on getting money from the power utility. I don't sell power to the grid because to do so would make me have to pay a large monthly fee. (Alabama doesn't do "net metering".) But I am predicting a 3% inflation rate in power rates per year. So even with my solar system degrading a little each year (and thus saving me less power), it's more than offset by the power rates rising (i.e. if it saves only 57.9% of my kWh this year it still saves me more than saving 58.5% last year because this year's power rates are higher).
4. Some of you are funny thinking power rates are only 10 cents per kWh. Yeah, I know that's what the power utility states, including in Alabama (10.6 cents). But the reality is way more after they add in riders and state tax. On my last power bill it was 13.6 cents per kWh (you see that nowhere on the bill, if you want to know it you have to calculate it yourself). That means it's 28% more than their stated rate. Once I realized that, and once I took into account an inflation rate of 3% (we wish), that's when my math synapses decided to look into going solar.
5. About starting the A/C. It depends. Part of my project involved replacing both my gas furnace and old A/C unit with a variable speed heat pump. My inverter can start that but couldn't start the old A/C unit. So now my heat pump is on the critical load electrical panel (which is powered by my solar system even if the grid goes down and my inverter goes into emergency power mode, assuming I have power from solar and/or batteries). Now, my system isn't powerful enough to go off-grid and stay off-grid, which I think was the context of powering the A/C. (Look, it's a two-story house. Even after the upgrade I predict having 85% to 95% of all power "free" from solar averaged across the year, not 100%.) But it's an example of how even just one inverter can do the surge power needed to start a large A/C unit if it's one that can start slow (like variable speed heat pumps do). I bet once I have two inverters working in parallel I could have started my old A/C unit in off-grid mode.