My biggest issue with storing data inside the browser is the lack of tools to set up filter rules for clearing or explicitly not clearing website-specific application data.

Looking at Chrome's Inspector, Application Storage has "Local Storage", "Session Storage", "IndexedDB", "WebSQL" and "Cookies".

If I decide to clear all this stored data stored for all the pages with one button press in the settings, how can I be sure I'm excluding something important? Or if I install a new extension which helps me manage privacy, how can I be sure that it won't delete all this data because I forgot to add a site to its whitelist?