What you wrote is essentially true of Li+ ion batteries (not truly green unless the electricity is too). The part I was missing was the efficiency of electrolysis being half that of Li+ charging.
Fuel cells can also run cars, and refilling is much faster than recharging. So you can build cars which can go long ranges with quick stops. But of course the infrastructure for hydrogen fuel is well behind even car chargers, let alone gasoline.
He was promoted.