It ain't the static loads...
As the owner of short stout Airstream with receiver hitch mounted to very solid frame rails by Prior Owner, I've been through same dialogues..
We did risk it all by adding bike rack and bicycle on trip to Salem last summer.. We've now switched to folding Dahon Espresso bike that can fit inside or on top of tow vehicle...
The static load is minor, as you noted, and you could park a generator on the platform for storage purposes, or even when camped.. The problem is that the moment arm and mass of a generator creates a strong bending moment dynamically when the rear of the trailer is bouncing over potholes, drainage channels, pavement joints, etc.. Many of the most notable failures occurred with 1970's models when Airstream owned by Beatrice and cost reduction efforts reduced margins for a number of rear bath jmodels with heavy tanks under rear bumpers... Still a design issue, however... Airstream not identical to aircraft monocoque, since bottom is open and attached to flat wood floor attached to frame, but any stressed skin/shell design is marginally able to handle impact of incremental weight levered out from CG in vibratory motion..
There are threads offering examples and pictures of mounts for spare tire under A frame at front, and for mount of generator on top of A frame behind propane tank(s), even if some mod welding is needed. These might load up rear of tow vehicle and tongue weight, but put less potentially harmful stress on trailer..
In Theory, there's no difference between Theory and Practice, but in Practice, there is usually a difference...