My plan for if I am in a party is this; If I see another player, and want to try to communicate, try using hand gestures first. If we can wave to one another without one or both of us ending up dead, then I will try using game chat to see if they have a mic and also want to communicate that way. It really does not take long to switch from party chat to game chat, and im sure I saw there was a way to toggle push to talk in game without going into any menu. It might have been down on the dpad?
Sometimes I can't communicate, sometimes I don't want to. Sometimes I am in a party chat and other times I am in game chat. I don't see there having to be an explicit reason people have to chat in game anyway, im sure you can get the gist of someone's intentions if you are paying attention to them and what they are doing.
Sure, it will make things easier, but communication is still possible between someone who is deaf and someone who isn't. Besides, you can't always trust what someone says anyway. If another player is raising their gun and lining me up in their sights, I don't think them singing "Kumbaya" is going to make me believe they are friendly haha!
Xbox won't be exactly the same as on PC, but it doesn't mean it will be lacking with player interactions in my opinion.