Just stating that doesn't make it true as well.
If I had a generator that I hardly need, I would keep it without fuel and oil. I would not store fuel at all (nearest gas station 4 minutes of driving). Also I would have a bottle of fresh oil waiting next to generator.
ICE engines do not require periodic running to "keep them in good operating condition". Fossil generator is just a small ICE engine.
Those generators come out factory and often stay on shelves for 5-10 years before they are sold and ran for the first time.
Same with lawn mowers etc.
PS: Every Nissan Leaf can run V2H device. But zero have it.
V2H actually is a thing in Japan. Nissan Leafs were used for those. Also, Generac generators perform monthly (?) running of the ICE engine to basically keep it "healthy" (a few minutes only).