IndexedDB is an accepted web standard and can store images and files. If you try to store too much information the browser asks the users permission to do so. There is no need to use the local filesystem API because thats not a standard.
As for not storing things, that still doesn't require the phone to be logged onto the network. The web client could just be another "device". If you're logged with the web client then the data is pushed to your browser. If you're logged with your phone then the data is pushed to your phone. This hack of making the phone talk to the web client to circumvent the limitation of only a single device per user on the whatsapp network is just silly. Telegram for example allows you to log with many devices and you can remotely disconnect other devices if you want.
We have full IRC clients such as irccloud.com, we have full email web clients such as gmail.com, we have XMPP web clients. The web platform can handle instant messaging. We have desktop notifications as a web api. We have IndexedDB as storage medium. We have websockets as communication layer. There is absolutely no need for the hacks they did.
