Are there any benefits to food that isn't favoured by anything?
It turns out there is an advantage to, at the very least, Carrots and Pogofruits. When grown in a garden, food like Cuberries and Mint Mangoes will only produce up to 15 of each in a single harvest, while Carrots and Pogofruits will produce up to 20.
This is particularly useful when feeding Fire Slimes, as any kind of food can be incinerated to produce ash.
While this makes me think a similar mechanic is in effect for Hen Hens, maybe with them breeding or growing up faster than their specialized counterparts, that is harder to test due to the random nature of egglaying.