As is right now I just don't see the Tesla home battery as providing enough output to be meaningful for anyone who's not facing extremely high grid prices and using a large solar install with the battery to pull from at night.
The 2kW output isn't enough to serve as a whole-house backup unless you're already a fanatic about conservation or are willing to run around killing high loads when you lose grid power, and the 5 hours runtime you'd get from the battery @ 2kW isn't enough runtime.
In my mind, the inverter add-on is only part of the wiring issue. Most houses have a central breaker panel that terminate all the circuits and any whole-house system would have to feed this panel (risking overloading the backup source and requiring manual shut off of any automatic loads that might kick in). Or, more sanely, do some extensive restructuring of loads so that light/must-have loads are on one panel and high loads are on another so that when power transferred you'd kill heavy loads automatically.
What would be nice would be a smart panel that could be programmed with never/always/switchable values for each circuit and the ability to set priorities for them so you could maximize runtime and guarantee power.
Further, I think the wiring practices of residential electrical need to get a whole lot smarter. I'd like to see a dedicated panel for each of: wall sockets, lights, appliances, and "high load" appliances like central AC, electric stoves, and electric heat with a dedicated breaker for each room services by those individual panels.
Currently residential electrical wiring practices don't do this at all -- they run the shortest feed from whatever place they can, resulting in outlets sharing breakers with lights and often crossing rooms. When we remodeled I mandated some outlets be on dedicated breakers and in both instances found those "dedicated" circuits fed to other places because it was convenient for them. I made them change them but it was a fight.