Why Didn't the Ascian... (POSSIBLE SPOILERS)

[CodeCass]

You misunderstand- We cant summon our Gryphon while running/falling because it's Mechanic Bound. In a Cutszene there are whole other Laws active such as summoning your trusty Gryphon/Chocobo. Same with Teleporting to the nearest Aetheryt.

Ah, I understand where you're coming from. The way I always thought of it was that we couldn't teleport while falling or running because the Teleport Spell takes quite a bit of concentration, and you'd have to be in a still, safe place before attempting it. Which is why we can't port while in combat or skydiving haha. With mounts I just assumed it was something similar, since you can't summon them in battle either; it just needs to be a "safe" place to bring them out.