There are known cognitive processes that come into play when the brain has to turn thoughts into communication, written or verbal. There are different modes, and thinking primarily happens in the Default Mode Network, but rubber ducking activates the language network, articulating thoughts into verbal and written words. This "just happens" is not random nor unexplained: it's a result of the way our brains function, and rubber ducking forces this switch.

It's also why various sources recommend writing so much: writing results in learning, or perhaps writing is learning.