It's mostly to mix up an aerial approach. So if you're in the air already and the opponent has their shield up in anticipation of an aerial, you can choose to aerudo instead. There are no true follow ups, and it is more difficult to cover multiple options due to the very little advantage (or possibly disadvantage) you receive.
It's also pretty inferior as an alternative to grounded choke. You mention being able to jump one frame before inputting, but Ganondorf's jump animation (jumpsquat) actually takes 7f before he is considered airborne. Not to mention aerudo is 19f start up vs Gerudo's 16f start up.
So a aerudo done at the earliest possible moment is 7f + 19 = 26 frames of start up, versus Gerudo's start up of 16f. The recovery time is also similar. Not sure if there's any range differences though
All that talking aside, TL;DR I don't use aerudo for many of the reasons above. However, if I'm already airborne it can be a situational mix up to aerials.