Yes, ish.

In a previous job we did code review interviews. And went the route you said due to the problem I said. And yes, it's a lot better. But what also happened over time was that the bar slowly raised. Because over time the "harder" pieces of that session started to seem rote to interviewers, they became viewed as table stakes.

Mind you this is true of any interview scheme that has a problem solving component to it. I'm not saying that the code review style is extra bad here, just that it doesn't solve this problem.