I suppose the stringing theory is not too far fetched, but I suspect that its just a rosy story concocted to hide the less romantic reason. I wager that the true reason is not more interesting than to reduce the amount of metal in the coin. In ancient times it likely was originated to save valuable metals (when the coin was worth the metal its made of), and to make smaller denomonations larger and more manageable.
The only way the stringing theory holds water is if every coin in those systems had a hole, and I don’t think thats the case. second if this method was so efficient more countries would have adopted it. I don’t argue that folks likely strung them together once the holes were there, but its merely a beneficial side effect than the motivation.