Tab storage

The idea is about connect session storage with contextual tabs.
Why? Idea was born to allow send tab to other device with progress of move, volume level, etc. Additionally, it could be used in more ways.
How?
0. By allowing to kept many session storage for site and allow to associate each with tab

  1. User could be asked, which session storage attach, when load page
  2. Page could be informed about need to update session storage on (before) tab close, browser shutdown or tab send to another device
  3. User could send tab to another device with full session storage, so settings was preserved, movie/music starts when stopped, etc.
  4. It could be per-page contextual tab. It will be more ordered, not a messy. User could have many contextual tab/profiles per-page, but without (or with) storing cookies.

What do you think?