Each trade is apparently beneficial, to irrational actors, with potentially large power/exploitability differences (eg lottery tickets are "beneficial"), and values that differ from what you might care about (eg Pedophile rings have some "beneficial" trades involved).

That, said, it's probably actually beneficial overall. Just that the simple proof doesn't get you there.

Each trade is beneficial, or it wouldn't happen.

Each trade may be beneficial to the parties involved (although even this isn't necessarily true for the ordinary sense of the word "beneficial"), but it need not be beneficial to the economy as a whole. Trades can have negative externalities.