Obviously we have a disconnect. The OP is specifically asking about straight airs, not rotation, that would be a whole other conversation.
For straight airs I would never ever teach a new rider to favor any edge.
AASI teaches to pop from a flat base
Snowboard addiction teaches to pop from a flat base
Jumping with Jussie teaches to pop from a flat base
I could make this list very long but I'll stop there. The main point is if your teaching a new rider to jump you should be teaching them the safest most effective way, which is off a flat base.
I can pop off my heels and toes and do a nice straight air, but I'm an experienced rider and I would never teach these methods.
I guess we are talking subtle differences here then. If you watch the SA videos even when they say to pop flat based it looks like he is popping off his toes to some extent. IME pressuring an edge(toeside) is always better and makes for a more natural pop off the balls of your feet, similar to what Cr0 is implying as well. I'm not a instructor though and so what I teach others may not be optimal. I always teach them to pressure the toe edge and pop with the balls of their feet. Seems to work well and sets them up for rotations as edge angles just need to increase to precarve into rotations.