> What benefits do we stand to gain from still having things run or be stored on a local machine?
Security.
Security.
[1] You say "cryptography". I say "Analog hole".
And about security as in privacy. I don't know what future holds. Perhaps you'd be implanted a token that you can use for accessing the data which can't be faked or copied. Who knows. I just wouldn't rule out the possibility of a "cloud world" completely.
I know there's no infrastructure in place (yet) but we're talking about some kind of future, not about today. It's certainly possible though. Even secured.