You hear something like this in electric-car design, except it's in the form of trailers, not onboard energy. And it's in the form of a genset, not extra batteries. Basically, imagine a Chevy Volt, except with the piston engine in a detachable trailer instead of under the hood. For daily use, you leave the trailer at home, so no dead weight. For long trips, you hitch it up, and presto, no range anxiety.
I'd be surprised if this would work in the general case, at least if you want to run continuously as long as you have petrol fuel. I got about 40-45 miles on my Zero at 70mph. Assuming a 9 kWh pack, that's about 14-16kW continuous power draw (and of course it will be more with a trailer). Generators that size weigh far more than 200 lbs. If you just want a range extender, say an extra 50 or 100 miles (and then you are stopping to charge regardless) then you can use a smaller genny, but it's only a partial solution at best; might as well tow extra batteries instead in this case.
I'd think cars would have the same problem. Perhaps some of the more sophisticated tech that has gone into e-vehicles could be employed in the genset*, but you'd need it on the ICE side as well for significant weight reduction. Also, you're paying a premium twice; once for the vehicle, and again for its auxiliary powerplant. Probably cheaper to put that tech into a better ICE for the car/bike itself.
(* For an example of the state of the art of the portable generator industry, they are just now using AC>DC>AC inverter designs that allow more efficient motor fuel usage, rather than running them at synchronous speed all the time.)