Let me see if I can clarify some of the points made here. Basically, there are two different ways to use a Tesla (or any PV brand) system: (1) you can stay on the grid and use the Tesla to backup the grid if it goes down, or (2) you can fake an outage and trick the Tesla into taking over and use the grid to back up the Tesla if there's not enough sun. Several Tesla reps and engineers say this is perfectly within design spec. We choose (2) because you won't save much via (1), since you are still using the grid for daily use, plus we like being disconnected from the grid because of how erratic the voltage is and the various jolts that come up the line, frying lots of stuff. The Tesla system can be setup so you can use either method, whichever works best for you. It requires a breaker that cuts the grid off from the gateway grid input, so if we open that breaker, the gateway thinks there's an outage, and we are now running on the Tesla and 99.99% of the time we get enough sunlight to fully charge the battery by 1-2pm or so, then run on the panels until sundown and then the battery takes over. The Tesla does this automatically. Wash, rinse, repeat.
So practically no grid is used and our bill is very low. If we want to switch over to method (1), all we have to do is close this breaker, now the grid is flowing into the gateway, the house is generally drawing from the grid, and the battery will charge up using the grid or the panels if you have some sun and be ready for the next outage. If the grid goes down, the Tesla goes on automatically. If everything fails, with one big switch I can put the whole house directly on the grid, bypassing the Tesla (but it's still running) or even plug in my generator, if it comes to that (another switch needed...def not a big deal) We also put the whole house on the grid if we want to do some welding or run the electric clothes dryer, but only for that. Since you are essentially running on the grid using (1), expect close to your normal bill. I haven't seen or heard of a residential setup using a single battery that I would prefer. We always have power. That's not that common here in Puerto Rico...the utility company is very borderline, their equipment is ancient and poorly maintained, and not everyone here even has a generator, much less solar. A gen should be considered a mandatory minimum to live here unless you don't mind cleaning out a fridge full of rotten food or throwing out food or meds, etc, no lights, TV, cell charging, etc.
As has been pointed out previously by ggun, method (2) requires a bit more understanding of how your system works and how to interpret the data from the app, which will tell you practically everything you need to know, including when to close the grid breaker if needed, etc. But you'll get a lot more benefit from your solar system the more you know how it functions. It's worth the time learning a bit about it.