I read back through one of the earlier drafts of the original Predator on here a little while ago, and there was one scene that never made it into the finished film that I've wanted to see in live-action ever since.
It was towards the end where Matheny (Dutch) and the Predator are in a huge log jam that's so big it's almost like an underground cavern, and they're basically at either end of a corridor with a waterfall dividing them and blocking each's view of the other.
The Predator starts using his vocal mimicry to call out to Matheny in the voice of a teammate he thinks could possibly still be alive, and Matheny falls for it, hearing the voice and calling back, moving closer and closer to the waterfall.
But then the Predator screws up and mimics the voice of someone Matheny knows for a fact is dead, and he realises he's been tricked and that the Predator is right there in front of him.
So you get this super tense scene that flips back and forth, where first you have the tension of the main character not knowing he's walking into a trap, and then the tension of having both characters know the other is right there, and who's going to make the first move.
So yeah, I'd love it is this new film got back to using the mimicry in a tense way again, because it's definitely a cool trait that only tends to be used once or twice in a film.