Honestly it seems that most of Web Standards are used mostly for fingerprinting - I think a small number of websites uses IndexedDB (who even needs it) for actually storing data rather than fingerprinting.
That's why expansion of web standards is wrong. Browser should provide minimal APIs for interacting with device and features like IndexedDB can be implemented as WebAssembly library, leaking no valuable data.
For example, if canvas provided only access to picture buffer, and no drawing routines calling into platform-specific libraries, it would become useless for fingerprinting.
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.