[ShadeTreeMech]

While charging the batteries, som efficiency is lost in the genset itself, and it's unlikely even that Honda generator will last its quoted timeframe on a gallon of fuel. (Look at the specs a bit closer, the quoted timeframe is for 50% total capacity useage.)

You'll also lose a bit through heat as the batteries are charged.

So why not attach the ICE motor directly to the wheels?

Yes, there's a bit of sarcasm involved, but there is an important thing to consider. Generating your own electricity is not subsidized by the government and isn't nearly as efficient as a professional power plant. I suspect if the miles per gallon used by the generator were figured, and it was the only source of recharging for the batteries, you would have an efficient vehicle to be sure, but not nearly as much so as when the batteries were charged by the house current.

I think a diesel genset would be the best choice for a range extender, but it would be nearly worthless in constant driving. It would be highly awesome for city driving though, assuming the weight of a genset would be better than the same weight of additional battery capacity.

Even in electric vehicles the laws of physics still apply. There is no free lunch. If you had a portable genset capable of recharging the batteries after they've been discharged plus driving the electric motor, it would be so heavy and consume so much fuel you'd be better off attaching the engine to a transmission and losing the electric drive altogether.