This doesn't make a whole lot of sense because people give up their phone numbers from time to time. I did this myself. My understanding is that someone who claims my number cannot access my past data. But if it is "stateless" then a phone number doesn't have to be the only identifier. They can also use email. Heck .. here is an algorithm ... use phone number 555XXXXXXX .. take a person's email address and hash it to XXXXXXX. Done!
Most people in the world don't (or barely) use email, specially in EMs. Also, you can access you email from many different places, you (usually) can't receive an SMS on the same number from many different places.
Another advantage of using phone numbers is that people actually have other people's numbers in their phone address books, which whatsapp uses. Very few people have their friends' email addresses on their contacts.
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.
