Horizontal is a simulated CESA. I suppose it could be renamed CESH.
There is definite danger, and potential life-threatening danger at that, in performing a CESA. You are relying on the student to exhale all the way to the surface AND to exhale at a rate that matches or exceeds the rate of lung over-expansion that they will undergo during the ascent. If they do it wrong (hold their breath or don't exhale enough), it's extremely difficult for an instructor - even when you've got them firmly in your grasp and you're going right up with them - to force them to exhale. Should they embolise on the way up, you are now faced with an immediate life-threatening situation rather than an "Atta-boy!!"
By doing it horizontally, you are eliminating the ascent, which eliminates the lung-expansion, which eliminates the danger of embolism. Another way to look at it would be that instead of considering it an ascent, you're teaching them how to swim and exhale over a certain distance. It has application both horizontally and vertically. But since we know there's embolism danger in a vertical ascent, this eliminates that.
And if you REALLY want to nitpick about mitigating risk, unless you have them swim side-to-side in the pool, do you have them go deep end to shallow or shallow to deep? In going deep to shallow, you're still doing an ascent (over the 75' length of a standard pool) since you're likely going from 8-10' deep to about 3' and then surfacing. Chance of embolism exists. If you go shallow to deep, and instruct them (assuming you're doing this with reg-in-mouth) to follow the bottom and stop when they hit the deep end wall (at which point they can inhale off of their reg), you've totally eliminated the chance of embolism.