Gas powered generators are designed to run efficiently for small shitty motors. Gas generators are not efficient. Especially if you care about emissions since they usually lack catalytic converters.

Making electricity this way, storing it in the battery and using it to drive a vehicle have their own efficiencies, all less than 100%. Also, these smaller types of generators aren't that efficient to begin with. So I doubt it.

Well, as far as I know Honda hybrids work this way.

The fun fact part is, this is could actually be pretty damn efficient if done well.

This is essentially how diesel–electric locomotives work (since almost a hundred years now).

An EV with a range extending gasoline motor could also easily be configured to run at peak efficiency with the added benefit of being within the aerodynamic envelope of the car instead of being a trailered brick.

That's how most diesel trains work. The diesel engines run generators that power electric motors.