Beyond managing your identity/s, the most compelling notion this brings to my mind is that sites should reduce transmission of redundant data: You specify the structure once then only the data is transmitted (what someone else referred to as "like iOS apps"). To an extent we are already moving in this direction with asynchronous update technologies, but rather than a next-gen browser, it seems like we need a next-gen language that places a primary emphasis on reducing wasteful transmission of redundant information. E.g., On iOS I update my FB app when there is a change to its structure and then I do so exactly once; Why am I re-downloading its structure in my browser window multiple times a day?
In particular, you can install these native apps and no longer need to download the UI again and again, instead just get the updated data. And access the past data even when you're offline.