Yes. this would be useful for gameplay.
No, emotes only are fine navigate through menus.
An issue I've run into with destiny, is usable items within your inventory. It's annoying when you run out of ammo and can't see any on the battlefield, then you have to go through the menu and hold square (or X) to use backup ammo you bring along. I'm not saying to get rid of the emotes, but being able to reassign them would be useful. Maybe holding a direction on the d-pad will let you be able to link things fast from your inventory, or reassign it as a hot-key. Or want to pop that bonus glimmer item sitting in your inventory? Assign it to your D-pad Up and use it instantly when you see a big event happening or a strike/raid you're about to start. This would save needless menu navigation in the middle of a battle, and it wouldn't necessarily get rid of emotes since they would be re assignable as well.
If anything it would just make combat a bit smoother and even allow for more emotes you could find around destiny for certain quests or beating certain bosses, even as rare drops. It just feels a bit basic and wasted controls the way they sit currently, when they could be so much more useful. Even if you prefer the menus as they are that would still be an option to use it that way, and leave D-pads for emotes only. I'm assuming there will be more inventory consumables than ammo and increased glimmer in the full game, and this would be a nice solution to fixing the encumbered system currently in use.