WhatsApp does not store messages on their servers. It's a clean passthrough from one device to the next. They only hold onto message until all clients in the group text or one-on-one text have received the sent message. So, if you have two clients using the same phone number, the system wouldn't know when it is able to delete the message. Right now the single phone receives the message and simply passes it up to the web browser. It's a simple solution that fits into their data model. They claim that they cannot get this working on iOS which prior to iOS 7 may have been true. However, on iOS 7 and above we can run code (even async network calls) when we receive a push notification so they should have been able to work with that API to produce similar results.
I believe you're wrong. This is how WhatsApp USED to work before they were acquired by Facebook. Remember how messages used to stay in the waiting (clock) state and you could delete them if the recipient wasn't online? Well now the first tick appears immediately because there's an intermediate server storing them for delivery and they can't be deleted from the client. It's similar to what Microsoft did to Skype.
I'm 100% sure that this wasn't the case. I'm not saying that there always was an intermediate server, but it definitely was before Facebook acquired them.
OK. I thought you were getting it confused with one of the message saving snapchat proxies (which then got hacked). But whatsapp is clearly not a replacement. snapchat may have failed to delete videos from the users device, but whatsapp doesn't even try.
WhatsApp used to even save snapshots of the database, for a week(?) I believe. In a SQLite DB. And deleted messages are not vacuumed. Recovering intentionally deleted messages off a user's phone was a trivial job. At least on the Android version.