I disagree. The IndexedDB was introduced as a permanent way to store data (which is not deleted after closing a website). As it is the only available standard for permanent storeage, I think it should be deleted only if the user asks to delete it (the same way you delete any other file in your computer).

Of course, browsers are free to do whatever they want. But the user can (and will) switch to the software, which does what he or she wants.