We do student panels for staff interviews too, their feedback is often insightful and complements the other feedback. We are looking to see how candidates interact with the students, rather than what their answers actually are.
I recently observed a student panel and the feedback was brilliant.... one candidate seemed dismissive of the questions and wasn't viewed strongly by the students. Another, didnt really answer their questions and seemed to have an agenda.... kept changing the subject back to what they wanted to say.... this one also didn't score highly with the students.
The candidates that they liked were the ones who took a genuine interest in them, were open and friendly and at ease with teenagers.
The feedback pretty much mirrored what the interview panel thought but it was good to hear that the students were on the same page.
In my school, staff panels and student panels form part of the process as well as a lesson observation and a task/ presentation.
We don't always do this for every interview, but would for a middle or senior leader or a pastoral job where the relationship with the students is a key part of the role.
The observer of the panel or the lead in the staff panel is the one to feed back to the Head/interview panel using everyones written notes which are kept in line with recruitment procedures.
The main interview holds the most weight alongside lesson observation and any measurable task.