http://en.wikipedia.org/wiki/Web_storage
https://developer.mozilla.org/en-US/docs/Web/Guide/API/DOM/Storage
All web browsers have had the DOM Storage feature for many years now. While there is usually an option within the web browser to disable its DOM Storage, way too many sites will malfunction if it is disabled. They store their global variables or other data there that gets used for painting, navigating, or the functions within the page. Way too many programmers do not test the return status of a function they call. Similarly, many web page coders don't test if DOM Storage is enabled before assuming they can use it. You can see in the web browser's console log all the errors in them trying to store or read from DOM Storage but their scripts have no error or graceful recovery. The result is the web site is unusable if DOM Storage is disabled and they have no alternate or recovery mode to use their site without using DOM Storage.
Yet DOM Storage is only required to properly render such sites when you are actually connected there. When you leave or are otherwise disconnected, their data they stored locally on your host in DOM Storage is of value (to them) only upon your return to that same web site. If you do not want to carry over a site session between web browser sessions then the content of DOM Storage is not required. Obviously DOM Storage provides a very easy way to track a user and their repeat visits.
I see no selectable option within CCleaner to have it clear out DOM Storage. Is purging that local data cache a difficult task? Or are users to rely on purge-on-exit features within the web browser to hope that the web browser, upon exit, will delete that cached data?