I think its obvious that a portable genset is useful when you don't have shore power available. The possible reasons for that are many, but hard to know if any of them would apply to you.
#1 is probably camping at a non-power site for longer than the batteries will last (recharging batteries). Applies to Walmarts and rest areas as well as campgrounds or friend's driveways.
#2 is the same as #1 but with an additional need for a 120v (only) appliance, e.g. air conditioner.
I think the lower fuel consumption notion is mostly myth. Fuel usage is almost entirely tied to power demand (watts used), not generator capacity. A 2000W genset producing 2000W consumes pretty much the same amount of fuel as an 8000W genset producing just 2000W. However, at very low power output, say 100W, the 2000W genset does have a modest advantage in fuel consumption.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL