The Mainstream Media wants to be able to be free to cut/edit as they please to be able to put their slant & spin on anything in anyway that best suits them. So they’d prefer not to have things such as video interviewed videotaped since that could be used to quickly expose them for what they are.
It’s the same reason that bad cops don’t like to be videotaped on duty - it limits the possibility of their commiting crimes or lying about their activities and findings.
I can't imagine anyone, private or public, being willing to be interviewed without making their own copy of the interview which they can bring out when the media starts clipping off answers or even mismatching questions and answers.