I guess if the point is for them not to store your messages on their servers once those messages have been delivered, how is WhatsApp to know whether to send a message to the session logged in from your phone, or to the desktop app with a different session, or to your work computer where you forgot to log out?
Being able to sync across all your devices requires they start storing all of your communications centrally, which defeats the whole information security model.
This way, you might not have the full conversation on each device - e.g. you write "a" to alice on your phone, turn it off, turn your pc on and receive "what do you mean?" from alice - the conversation is otherwise empty.
That's not a good UX.
You'd have to store the chat history somehow - and thus loose the privacy aspect of not storing it.
Being able to sync across all your devices requires they start storing all of your communications centrally, which defeats the whole information security model.