Don’t forget transfer switch’s have been around far longer than any EV or battery storage. The term generator means exactly that – a diesel/petrol generator, allthough they can be used for anything that require 2 seperate power sources.
All thats needed with a generator in a inlet box connecting the genny plug to it and is wired to the consumer unit for example (similar to a socket). A generator outputs the same power as the grid. In the event of a powercut an automatic tranfer switch would switch to the generator position and automatically start the generator.
With an EV or battery storage and inverter would be needed, in the same way an inverter is needed (cars onboard charger) to convert AC to DC or vice versa. This incurs losses during the conversion. A generator doesn’t, as there is current conversion.
If your car is capable of V2L, there is no reason it can’t be connected to the generator input of an hybrid inverter and setting limits in the hybrid invertor to stay below the car’s maximum continuous V2L. However in a similar way as a petrol or diesel generator you would have a “socket” externally to connect the vehicle V2L cable into.
Don’t get confused with earlier comments where the MG4 has something like 2.2kW V2L but, you suggested people were pulling 7kW. This is different and requires a bit of trickery, by using a resistor in the circuit, the V2L load can be increased.