There was no "old barter system" the way modern people think of it. The idea that pre-commercial economies operated on a "barter system" in the sense that people are directly exchanging goods of similar value is just a simplifying metaphor early economists made to explain how commercial transactions work.

Pre-commercial economies operate more like gift economies. It's not so much about trading objects based on their valuation, it's about doing favors for people with the expectation that they will do favors back for you. It takes strong bonds of social trust and cohesion for this to work. Everyone has to have a sense of obligation to pitch in for the community.

The bartering only comes in as a form of collateral when dealing with outsiders (people you don't trust as much). This is why the earliest form of exchanges in this way were tied to marriages (e.g. dowries, bride prices) or interactions with other political groups (e.g. treaties, armistice).

Barter doesn't actually work, it's basically just a format for giving collateral to make sure people don't welch on deals. Normal currency already solves that problem way better than trust chains based exchange does because the value is obvious and exchanged up front without having to go through any clearing-house to be validated.

So at the dawn of agriculture, people weren't using barter -- they were using credit unions.

Literally chisel some hash-marks into a rock so people don't "forget" and problem solved.

No.