This ties into a Midnight theory I've had floating around in my mind for a while now. I always planned to write a thread on it, but I've procrastinated on it forever and I really doubt I'll ever get around to it, so might as well just do it here:
So: let's just assume that the Doctor and Time Lords have the super power of simulation – they don't need math to predict the universe, their brains are large enough to handle it. They can more-or-less perfectly extrapolate known variables into the future. That's a topic for a whole other post I'll never write, but I have sufficient in-universe evidence, so let's just roll with it for now.
The Midnight creature mirrors this ability. Under my theory, it was a sort of artificial superintelligence designed to very quickly build very accurate simulations (by copying the passengers' voices), choose the simulation would most likely lead to its survival (focusing with the Doctor), and fucking with timelines so its simulation of the Doctor predicts him before he ever actually acts (taking control of his voice).
Who would need to build such a perfect mimicry of Time Lord power? Someone who needed a strategic advantage, who needed to gain equal footing with Gallifrey in some sort of conflict. Trying to beat the Time Lords at their own game. And who could that be?
Well, the Daleks! They're no stranger to biological engineering and manipulation, as we've seen time and time again with their human clones. During the Time War, they expanded into self-manipulation to make the Skaro Degredations (per Engines of War); a foray into artificial intelligence in their fight against the enemy doesn't appear too much of a stretch.
However, this particular weapon was never used in battle, or else the Doctor would have recognized it. Why didn't the Daleks utilize this powerful tool? Simply because they were as victim to the perils of AI as we are today: it was too intelligent, and they couldn't control it. Rather than risking the introduction of yet another side to the already-endless conflict, they abandoned it on some unlivable planet, deprived of useful resources.
No useful resources, that is, until a particular human leisure transport wandered through and disturbed it from its dormancy … and not only did it survive being sucked back out into the hostile environment, it's now aware that it's no longer alone on Midnight …