JWP (JSON Web Proofs) are meant to provide for privacy. I'll give an example of digital documents used as credentials.
Imaging a health record containing your vaccination history. This could be signed and shared as an interchange record between doctors. It could also be used as a proof of vaccination - this is what SMART Health Cards were.
However, there is considerable information in those records that I may not want to share - not just that I _was_ vaccinated for instance, but when and where, by whom, from which batch, potentially under what insurance. It is also common to have personal information like full name and potentially home address.
So you may want the ability to select which information is disclosed - you can do this with traditional signature and hashing algorithms by building a Merkle tree or nesting signatures with ephemeral keys. The document still has integrity, but only some subset of the information has been shared.
The signatures and hashes from a classic algorithm serve as potentially trackable identifiers as well. Newer algorithms like BBS provide unlinkability, where presentation of the same source document multiple times does not allow for parties to correlate my usages.
Finally, you also may want to disclose derived information - such as just that I have a vaccination in the last x months, rather than the precise date or location, or just that I'm of legal age to purchase alcohol in my country, rather than my birthdate. These sorts of predicate proofs are also of interest to the group, although the algorithms and representations aren't as far along yet.