Rob, I can't remember ever kneeling down to take a bearing - have I been doing it wrong?
I have. Back to the wind on the Cairngorm plateau, goggles fogging up and great big mittens slipping on the bezel.
As for teaching it, no I don't say they have to kneel. This little addition to the thread has made me have a little think, which is something I like. I am an experienced Mountain Leader, a Course Director for Gold National Navigation Award Scheme, active with Mountain Training assessments, and a competitive orienteerer and coach, and I've never met this as a hard piece of advice.
I can see what the author is getting at in terms of having a stable point to help stop map and compass slipping around when trying to do it. There is also something to be said for reducing overload. It is something I have done on occasion when the elements are against me. However, as a routine thing I don't see it as necessary. With a suitably-folded map and a good thumb grip holding the baseplate in place while you turn the bezel, it should be fine. A simple check that it hasn't moved before taking off the map should be part of your process anyway.
You know what the photo reminds me of? Army instructional manuals. Possibly the author is thinking that they'll be needing to juggle map, compass, chinagraph and so on to triangulate a position. Whether actually doing that or just having fun in the hills, if I have to go to that level I'm putting the map on the ground and lying on my belt buckle behind it.