As the text states, the Entertron gives you a full night's rest in moments, but still leaves you hungry. It only recovers your strength, it will not give you nutrition. They eat what they can, the get no substance from the Entertron.
Personally, I think the Entertron is just a game mechanic to replace inns. If you have a lack of food, you want to sleep as long as possible so that you don't feel the pangs of hunger. Getting a full night's rest in moments will mean you're awake for longer thus hungry for longer. Yes, you can scavenge for food more, but you won't need to scavenge as much if you're asleep.