Well if the idea is a process that works under duress, then your analysis is flawed.
The hand naturally finds the mouth. When replacing your regulator, if you grasp it by the case, the mouthpiece will be oriented correctly so that your hand will naturally push it in your mouth. And if you need to use the purge button, then the button is right under your palm. All you have to do is squeeze or push.
On the other hand, if you are grasping the 2nd stage by the hose, the mouthpiece might be turned up, or turned down. You'll have to pause to look at it, and possible use your other hand to rotate the 2nd stage to orient the mouthpiece. Otherwise it could take 2 or 3 attempts to get the mouthpiece in your mouth.
On the other hand, when donating a 2nd stage, you do want to hold it by the hose so the recipient can grasp the case and do the above.
If you are the recipient of an air sharing procedure and you have been trained to always grasp a 2nd stage by the hose, and the donor is already holding it by the hose, then you have to stop and think before you grasp the 2nd stage, elsewhere.
On the surface, it sounds logical to just say: Always grasp the 2nd stage by the hose, whether you're putting it in your mouth or someone else's. But when you really analyze the actions required, it doesn't hold up to scrutiny.