I think the logical fallacy is thinking about the economy as a steady state system. At any given time there are finite resources, so it is "zero sum" in that the pie is finite and slices can only be shared once.

That's not zero sum. The pie can be 100% finite and yet, while everything else remains equal, two people can both benefit and be happier at the same time by simply (and voluntarily) exchanging a good or service between them, because they value those things differently at that point in time.

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.

I agree :)

Trading the goats for chickens doesn’t necessarily lead to more wealth though, that would depend on using the chicken or goats to improve productivity.

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.

Entities without competition inflate prices until they capture all the extra new pie.

You receive increase in salary from your boss one year and next year it gets eaten away by monopolies like healthcare, education, housing and landlords.

Rent seeking may be zero sum, but the economy as a whole not. If we banned rent seeking the economy would likely grow faster. You could argue that's changing the game, but the economy is a weird one in that changing the game is part of the game.

We do ban a lot of rent seeking, though. For example, theft and fraud are rent-seeking activities. So the sorts of rent seeking that you still see are the ones that are hardest to ban.

Banning rent seeking doesn't work. Christianity tried banning interest and it just causes non Christians to offer lending services which then results in xenophobia. Interest payments partially derive from the liquidity services provided by market participants (think long opening hours and storing products ahead of time). Money effectively becomes a public institution where people voluntarily give it value in the form of liquidity services. That public institution is then kept in private hands who lend out money and then get to market these liquidity services as if they provided the public institution themselves. Basically someone else does the work and you get to benefit.

The answer to this problem is a demurrage fee on cash. Banks can then compete by offering the ideal negative rate that is in proportion to the liquidity premium. Banks can then use this fee to pay for liquidity services.

Is anyone doing this? No and I don't think it will happen in the next 30 years.

So rent seeking doesn't work because a long time ago one subpopulation banned it and it didn't work for the population as a whole? That's ridiculous. It's like saying prohibition in the US didn't work because booze was legal in Canada.