I have to admit, that I never looked into the technical details of full disk encryption

If I understand you correctly, they are using the same key for all the data and with larger amounts of data statistical analysis becomes feasible
Did I get this right?

Couldn't that be solved by using a root key + salt per block/sector/file/whatever?

I'd still only need the one root key and with every block the actual encryption key changes

I was thinking about perfect forward secrecy and that was the first thing, I could come up with

But, I'm absolutely not a crypto/math guy, so probably I don't know enough to really add something to the discussion/solution...