Context is key. The systems we choose to employ on our climbs will be more or less effective depending upon the specific circumstances we face. So, I am hesitant to use the words "always" and "never" when it comes to climbing techniques. The full video, as an example, gives four exceptions to the notion that we always belay a leader from the harness and a follower from the anchor.
Follow this link to the full video and accompanying blog post.