This way, you might not have the full conversation on each device - e.g. you write &quot;a&quot; to alice on your phone, turn it off, turn your pc on and receive &quot;what do you mean?&quot; from alice - the conversation is otherwise empty. 
That&#x27;s not a good UX.
You&#x27;d have to store the chat history somehow - and thus loose the privacy aspect of not storing it.