What I don't see discussion of (regarding batteries) is usable lifespan. For most things a 6-year payback isn't too bad and even 10 years could be acceptable in some circumstances, but there are two problems with this regarding batteries. Firstly battery capacity decreases slowly over time, as anyone with a 5 year-old mobile phone, laptop or Nissan Leaf will tell you. This means that a system which is initially capable of storing (say) 13kWh could store less than 10kWh by 5 years, possibly less. This reduces your capacity for timeshifting and therefore extends the payback period.
Secondly, Lithium batteries have an effectively finite number of charge-discharge cycles - mostly to do with this reduction in capacity. A friend is very keen to buy an electric car, but can't afford new (and is reluctant to rent), but all the sensibly-priced second hand cars he has seen need new batteries, which changes the equation significantly. All the evidence points to car batteries being effectively "dead" in the 7 to 10 year window, so a 10 year payback is going to end up as a net loss, and even 6 years is of marginal benefit. A friend of said friend is considering building his own battery storage using Lead-acid traction batteries, but those things also have finite lifespans - similar technology batteries in our UPSes at work need replacing every 5 years or so.
And this ignores the likelihood - especially as more people ditch tax-raising fossil fuels for (at the moment) tax-exempt electricity - that over time electricity prices will rise while incentive schemes will reduce.
A possible upside is that if you can just about - or very nearly - make your money back before the batteries need replacing, those replacement batteries should cost less (prices are generally reducing, plus some of the "infrastructure" you had to put with your original set can be re-used) so payback for the second and subsequent sets should be slightly quicker. Then again, electronics also wear out over time, so even the controls and inverter will eventually need to be replaced.
As a different friend was opining yesterday, we're at a point with reducing incentives and still relatively high costs where most "environmentally friendly" technologies are not going to save the average homeowner any money at all. Some (heat pumps being the obvious topical example) currently cost more over their lifespan than the traditional technologies (i.e. condensing gas boilers) they replace. You need to be willing to pay a bit extra to "save the planet" in terms of reduced emissions of CO₂ This is likely to change over time, but the days of bunging half a dozen solar panels on your roof and waiting for the cheques to roll in are well and truly over.
Regarding power outages - I don't think any of the existing systems are capable of riding out power cuts without some significant electrical work in the house. For example, I believe the Tesla Powerwall 2 has an inverter capable of 5kW continuous. In order to allow this unit to run the house in the event of a power cut you would have to be able to "shed" loads - so the Powerwall could be connected to lighting circuits, the circuit which runs the boiler and heating controls and maybe one segregated sockets circuit, but it must be kept well away from electric showers (8 - 10kW), immersion heaters (typically 3kW), cookers (typical oven is 2kW, rings are 1kW, 2kW, 3kW), and you'd want to be careful with microwave ovens (2kW+), kettles (2.5 or 3kW), and those "white goods" (dishwasher, washing machine, tumble dryer) which typically have a 2kW heater as well as motors etc. Doing this means re-arranging (replacing) your consumer unit (fuseboard) and/or re-routing or re-wiring some circuits. Older installations, for example, might have the central heating system run from a general sockets circuit. It's not that you couldn't run the kettle from the Powerwall - the specs definitely imply that you could - it's more that you need to be able to guarantee that you are not running the kettle, the microwave, the dishwasher, the fridge, the lights, the TV and the computers at the point the grid goes down, so that the poor Powerwall doesn't have to try to pick up 10kW.
It's also a whole other kettle of fish regarding grid connection if you wish to ride out power cuts, in order to avoid feeding energy back into the system which is not only dangerous for your equipment but could also be dangerous for people working on the lines. In the case where your house receives an earth via the neutral connection or the cable metal sheath you have also to consider what happens if the power cut is due to a severed line. Most grid-connected systems are mandated to shut down in the event of a loss of mains, and this was a contributory factor to that massive (but very brief) power cut a couple of years ago (August 2019) which stranded all those class 700 / 717s.
I'm not saying it can't be done - I know it has been done - but it's not as simple as plugging in a battery and suddenly you are making dinner for the whole street when there's a Sunday lunchtime power cut.
M.