Batteries keep getting cheaper but are unlikely to get to where it’s more affordable to store a month’s worth of electricity than just buying some generation.
This wouldn't work. The reason isolated units can inject electricity back into the grid without issue is that they can observe frequency. If a blackout occurs, this information is gone. You need to perform a black start, which can't be done by isolated, uncoordinated equipments.
Many of the PV systems you can buy from the big players (SolarEdge, Tesla and more) support this, often calling it "whole home backup".
Same principle as having a generator with an interlock.
I know what you're talking about though: I think that more applies to generators that are operating with megawatts and take time for turbines to spin up and stuff. Microgrids are normally instantaneous battery buffered type things. They can instantly deliver power at the frequency range mandated for the national grid.