I think the pushback here is from the following:
1. Because it is so dynamic and subjective, it is very hard to systematize this kind of interview, which makes it very hard to work into a repeatable or scalable process. The need to compare incoming candidates is an unfortunate reality of the industry for many companies.
1b. It is basically impossible to control for bias and things like "was the interviewer having a good day".
2. This kind of interview overly rewards charismatic speakers -- this is partially ok, depending on the role, because being able to speak accurately and cogently about the work you're doing and are going to do is part of the job (especially for staff+ engineering). It isn't necessary for all jobs, however.
3. Many people aren't good at driving this kind of conversation for whatever reason. When it goes well it goes well but when this kind of conversation goes poorly it reflects badly on the company.
4. People Ops want more control then this gives them, across many dimensions.
