Pure speculation, but it sounds like they're relaying everything through the handset. That might explain the lack of iOS support, as background processing is still somewhat restricted.

That might also be related to how they're now encrypting messages on the handset after partnering up with Open Whisper. https://whispersystems.org/blog/whatsapp/

Edit: this is also pure speculation.

Whats App uses your phone # as authentication and identity. There is no username and password. So connecting to your phone is only way to verify you are who you are.

But surely once verified it should be possible to use the app without your phone? It works that way with Telegram.