Why do Interviewers talk over Interviewees ?

Marmin

I suspect it might be a reaction to interviewees that are clearly not answering the question.

Exactly this!

Fiona Bruce on Question Time does this all the time, particularly to Conservative panel members, or more right wing panel members. The Labour panel members are allowed to speak freely. I noticed last week that she was particularly bad with the Conservative politician. We want to hear all the points of view, even if we disagree with them.
I dislike her on Question Time and wish she would be removed and replaced with someone who would let all the panel members speak.

I suspect it might be a reaction to interviewees that are clearly not answering the question.

I think it must be a memory problem.
They have forgotten what their job description is.
Very irritating.

Naga Munchetty on BBC Breakfast is one of the worst. I can't stand her.

You have answered your own question.
It is a tried and tested technique of the Today programme, and other BBC interviewers, to ask a question and then deliberately talk over the interviewee so that their answer is not heard and/or deliberately interrupted. Emma Barnett did exactly that on Woman's Hour; as far as she was concerned it was an audition for Today.

Nick Robinson, who considers himself the BBC's greatest asset, wrote in newspapers posing the same question to try to discover why listener numbers were falling without the slightest inking that he, and others of his ilk, were the problem.
We are not interested in the interviewer but they they are; making themselves the story is the biggest crime in journalism.

I always thought Michael Parkinson was guilty of this. Never understood his appeal.

They all want to be the next Paxman I think.