I'm not a pro as I only assist and with post-AOW students. I ascend horizontal, on my dives or when assisting. And I initiate my ascent while horizontal. We try to steer our students that way as a more refined ascent method. Buoyancy/Trim/(Ascent/Descent) is the lecture I created and gave as part of my DM training.
I think the complication is saying:
A) 'stay a bit more buoyant for more of your breathing cycle so you start to ascend'
while saying
B) 'do not ever hold your breath, specifically do not close your glottis.'
That I can tell, A is the only way to start a horizontal ascent, assuming you do not just add BC air just to vent it once you start, or kick up briefly. Yet 'lungs a bit more buoyant yet not breath holding' is a delicate message. Particularly as an action to start an ascent, which will expand your lung's air.
Emphasizing the small size of our normal tidal volume relative to our full respirator range and that only a small shift of volume or timing is needed to start the ascent, and thus stays far away from a dangerously full lung has seemed the key. But it is a bit past 'breath from this, don't hold your breath'.
Lung volumes - Wikipedia
With some possible types of ascent being:
1) 'push the air-add go-up button' - BAD. A great way to become a missile.
2) Vent a bit (as an anti-missile measure), and swim upward. Very preferable to 1, and easily understood. Yet depth control via kick strength modulation is not a simple task, particularly if you get distracted.
3) Let your breath cycle go a little positive on average, vent as you ascend, horizontal for more drag and thus easier depth control. Lots of advantages, but a more subtle message.
When and how to teach..., I just assist. That training thing is up to you great instructors
. It does sound as if the OW curricula encourages horizontal positioning in general.
ETA: that is a 2013 video. Are there some more recent demonstration videos from agencies?
Their, Dive Training Magazine, 2017 video seems to show a bit more slanted upward approach, though they are definitely not horizontal.