You can use a browser extension like "Local Storage Editor" to see the contents of the Local Storage of a website. So far, I've seen it used for caching long-life images (like on gmail), or used as another way to do logins instead of cookies.

I'm with you up to the bit about canvas. The problem there is that if you want hardware acceleration then either you can't permit services to read back what was rendered (why do they need to do that again?) or else you're inevitably going to leak lots of very subtle platform specific details. Personally I think reading back the content of a canvas should be gated behind a permission dialog.