Vehicle by definition can't be connected to the house constantly. I can imagine this lowers need for house battery size, but not need for it's existence.
House power consumption is very random.
There is typically good connectivity between houses. That means even if your EV isn't home, the other EV's in your street can send your house a lot of energy.
Unfortunately anti-islanding rules from power companies generally disallow you using the power lines between your house and a neighbours while the grid connection is disconnected elsewhere.
These rules could be adjusted though - although it would take a lot of systems design work to ensure power system stability and re-synchronizability even with every possible combination of islands.
It's more about safety than reconnection: when repairing lines, it's much more manageable to "lock and tag out" the upstream side than all the distributed generation, especially in emergencies.
Any lines being worked on will be shorted (ie. all conductors joined together and to ground).
As long as that is always done, islanding doesn't present any human safety concerns.
That is normally done anyway, because plenty of utility breakers will automatically try to reconnect every few minutes (allowing some grid scale failures to repair themselves with no human involvement).
But when the vehicle is connected, the user is typically at home. So there's a convenient relation there.
House power consumption is random because it's not designed to be predictable. It's trivial to have a washing machine and heating that prioritize energy consumption whenever the EV is connected, or grid energy is affordable.
Unless you have more than one person in the house…
But in general, yeah, when you _need_ the battery, maybe you just need to figure out that you don't need to drive that day/hour.
The other advantage of a car, is that it would allow you to bring in power "from the outside", go to somewhere where the grid is still working, charge up, then come back. Of course, you'd hope to be back on power before this was needed!
