And in both cases, you're carrying the full weight of two motors at all times. It's sort of like a Tesla carrying a gasoline can and a generator just for range anxiety. (In fact, that combination would weigh less than an ICE motor and fuel tank.)
However, if you look at the mpg figures of, as an example, Toyota Prius with similarly sized traditional car you will notice that it indeed is worth the extra weight.
not having to lug a traditional gearbox around
You mention the Prius. Are you unaware of the complexity of its complex, heavy drivetrain?[1] Much heavier than even a traditional gearbox.[1] https://en.wikipedia.org/wiki/Hybrid_Synergy_Drive#Transmiss...
The drivertrain in the hsg is pretty much tje electrical motors. I did not say it is lighter. I said some of the weight is offseted by the fact that the ice part doesnt have to lug all the traditional components. Not completely offseted, just helped a bit.