I installed a 2.2 kw inverter on my truck. It's the best $300 upgrade I've done. The alternator has no problem keeping up. I use an induction cooktop off the tailgate when camping or doing a long road trip. You don't need to buy a new truck to get this.
That is great to know. Thanks! Currently, my main use case for my generator is running a 240V well pump that knocks 5000W honda generators over. (PG&E has taken > 2 years to run a wire ten feed and install a meter, for ... reasons)
Future me will likely have use for a “mere” 2.2KW generator though, and I’m really sick of lugging a > 200lb generator around.