It is already happening. The whole deep learning thing is no joke. They cannot replace human, but can achieve close to or better than human level of performance in certain specific tasks. Before that, close to human performance is never achieved for certain tasks, and largely considered impossible in near future just 5 years ago, like image recognition/playing go/speech recognition.
It is already eliminating jobs, gradually, not overnight but steadily, and this time it is from higher above, say, Wall Street traders.It is very easy to see there is a trend out there, that data + smart algorithms is going to take over a lot decision-making processes, that currently belongs to analyst.
The theoretical limitation of AI is bullshit. We don't get know what intelligence is, how do you think we quantify and draw a line around it?