As somebody that gives both phone interviews with a shared typing environment and whiteboard interviews, there are some problems I can only use with a whiteboard, but no problems that I can only use with a typing environment. In particular, whiteboards are significantly better at letting candidates describe what they're thinking about the structure of a problem before (or instead of) actually writing correct syntax. When someone is sitting in front of a computer, they have a tendency to either jump straight into coding or try to describe their thoughts in a giant block of comments, neither of which is very productive.
Maybe it's just our phone interviews that allow us to focus on higher-level concepts in person, but I've really never found a candidate who did poorly on a whiteboard but seems like they would have done well on a computer. If anything, it's the inverse where candidates jump straight into code, to their own detriment, when placed in front of a keyboard.
The trouble with whiteboards are that some people think nonlinearly. If I'm writing an algorithm, I may write the "middle" first. On a whiteboard, this means I have to guess how much blank space I need to leave in various parts of my code so I have room to fill it later. I almost always guess wrong. On a computer, this is not a problem.
Now while you may be aware of this and not give the candidate a hard time for not leaving enough space, I read a Medium post once written by a Google employee with tips on doing well on the interview. He explicitly highlighted this problem, and literally encouraged candidates to learn to think and write linearly and not leave these kinds of blank spaces.
Maybe it's just our phone interviews that allow us to focus on higher-level concepts in person, but I've really never found a candidate who did poorly on a whiteboard but seems like they would have done well on a computer. If anything, it's the inverse where candidates jump straight into code, to their own detriment, when placed in front of a keyboard.