One concrete privacy improvement is to identify subsets of existing functionality that are widely used and can be mapped to a separate permission, or no permission. Then, most extension writers can request that specific permission.
An example is Safari's content blocker API. They've designed it so well that the content blocker doesn't know what it's blocking, or what sites you're visiting. Apple didn't merely reduce the amount of private information collected; they eliminated it.
Another example is iOS, where a permission is needed to access all contacts, but if you just want to pick a content (say to share a document), you can invoke the system picker without needing a permission.
The web needs to adopt such privacy-sensitive subsets of permissions in addition to a blank cheque "access all data on all sites".
Disclosure: I work for Google, but not on Chrome.