To Kill Two Birds With One Stone

Why is this idiom in so many languages?

The idiom ‘to kill two birds with one stone’ means to achieve 2 objectives with 1 action.

It’s interesting to note that this idiom and its equivalent occur in many languages around the world.

In Chinese, it’s 一石二鸟 (literally, 1 stone, 2 birds), 一箭双雕 (literally, 1 arrow, 2 eagles), or 一举两得 (literally, 1 action, 2 merits).

In French, it’s faire d’une pierre deux coups (literally, to hit twice with 1 stone), so what’s being hit is not specified.

In Italian, it’s prendere due piccioni con una fava (literally, to take 2 pigeons with 1 bean).

In Japanese, it’s 一石二鳥 (literally, 1 stone, 2 birds, exactly like one of the Chinese versions).

In other languages, the referred animals are flies, like in German; rabbits, like in Romanian; or hares, like in Russian.

I have 2 questions.

1. What is the language of origin of this idiom?
2. Why is this particular idiom, or the equivalent thereof, and not other idioms, so prevalent around the world?