(I don't know the answers to how to interview in this brave new world, but I'm increasingly skeptical of forbidding tools that people will be using for the job.)
To write code (even with the benefit of AI) effectively you need a mental model of the systems you work with, reading the chatGPT response doesn't prove you have that.
The hard part is selecting good questions that act as reliable predictors of actual job performance. Very few hiring managers can do that reliably, although many fool themselves into believing that they can.
That said ML models have gotten to the point where I'd have to disagree with OP that this approach will necessarily filter their use. However there are plenty of available mitigations, from latency of response to requiring a video feed that fully covers the candidate, his screen, and his keyboard.