That's an interesting idea, but I can also propose that money evolved from finding ways to get other people to help you:
So little Joey comes over to Gramma Hilary and says "I'm hungry, give me one of your many chickens."
Gramma Hilary says to Joey "Take these buckets to the river and bring me some fresh water, then you can have a chicken."
Joey replies "There's too many buckets, I'll be going back and forth to the river for a long time, but I'm hungry now."
Gramma Hilary says "Tell ya what, you make two trips to the river, and I'll have a chicken all cooked up and ready by the time you're done."
This is barter and trade, a direct exchange without an intermediate currency. And it seems likely to me that these trades existed before money
Well I base my understanding of economic relations on real world practice by my people, the New Zealand Maori, not on some hypothetical scenario. Perhaps it may at times transpired as you speculate, but many studies by both historical and contemporary anthropologists found that it in pre-industrial societies it was often poor manners to demand reciprocation immediately and instead pretend that providing for other's needs is a gift, though it was implicitly acknowledge that the return would be in excess of that provided by the giver at some later date. It was a way to build relationships and bring people together.