Next door to where I was recently staying I talked to some farmers that grow rice. They live a subsistence life, barely earning enough to survive by selling their rice. Trading their rice (equivalent to the goats or chickens in your example) does not make them wealthier. No matter how much rice they trade they aren’t going to get a bigger slice of the pie or make the pie bigger. They can’t grow other crops without investment in education, seeds, and technology, which they can’t afford.
So in that kind of real world scenario you cannot simply trade what you have or produce to increase your wealth. And for most people they don’t even own the chickens or goats or whatever. They don’t even own the land they live on (land is absolutely zero-sum). Increasing their wealth requires outside investment of education or technology, which isn’t trade but charity/redistribution. And not surprisingly, the way that has happened has been through government investment (redistributing the pie).
The Robinson-Crusue Econ 101 hypotheticals are divorced from the reality of economic development.
If I have 10 chickens and you have 10 goats, we can exchange between us and each of us would simultaneously benefit more from having 5 chickens and 5 goats each, even though the pie hasn't changed.
Or maybe I prefer to have 8 chickens and 2 goats, while you prefer to have 8 goats and 2 chickens, and both be happier as a result by exchanging between us while the entire pie has remained exactly the same.
So happiness/usefulness/value was created by the exchange of goods and services even though the pie hasn't changed at all.
Also, these preferences can change over time, so value can continue to be created even if the pie doesn't change.