A friend of mine, when asked to implement an AVL tree, actually asked an interviewer when the last time he had to implement an AVL tree on the job was. He wasn't hired.
The department should run the interviews through their own employees first. If some questions cause an "interview anti-loop" (a set of other employees S who would not hire E) it's time to revise those questions.
Revise and rehearse these practice interviews within the department, and do it blind, until all of S are willing to "hire" each other for their respective roles.
Most of the time you see the resume a few days before. They may say a few things "don't say this don't say that". (hr)
Most companies take the rejection as a point of pride. "We've rejected 100s of candidates."
I don't like the structure, I think it's very flawed, but asking you to do something you do regularly defeats the purpose.
They're not looking for someone that is eager enough to show they're willing to work through it even though they have no idea to proceed.
They are looking for someone that got lucky enough to be ready to answer that particular problem, but won't stand up to them that the ask was a bit too much for a reasonable interview that is intended to see if you're a fit for the company and skilled enough to get the work done.
They aren't looking for someone that will dress them down to tell them that's incredibly insulting to ask something that took an academic a long time to come up with a solution for that. [Although a rough approach and fairly unfriendly. That shows a lack of desperation, confidence on the knowledge, and a good understanding of the difficulty of the task at hand (heck that's a good signal for won't underestimate points during planning)] (There's a singly linked list question that amazon used to ask that qualifies for this)