All those shiny skyscrapers that the banks build? It's for trust, along with a good deal of banking licensing requirements and regulation.
The example with the farmers' fields is quite valid. We forget in our relatively well-governed western nations that some governments really can't be trusted to simply keep records straight and not 'lose' vital documents, in cases where bribes abound.
Another example is foreign exchange trading settlements; I can't trust that if I send you $500mn in swiss francs, you'll actually send me the equivalent settlement in USD. You might go bankrupt half way through the transaction. And so there exists an expensive jointly owned escrow bank for exactly this purpose, CLS bank.
I'm sure there are many other examples, but the point is, trust is actually quite expensive.