Why attribute and identity providers need to be separate roles

A typical configuration of an IdP is to authenticate users against a directory that contains both credentials and attributes of users. The organization operating the IdP is responsible for maintaining the directory. It it obvious to assert both the user's identity and her attributes at the same time.
However, there are use cases that need different models:
A. AP and IdP are different legal entities. E.g. The AP is a national authority to assert the role of a health are provider such as general practitioner, but does not provide IdP services. This is a common case in European electronic health record programs.
B. There is no 1:1-relationship between IdP and AP. The AP might be a source of authority for a certain kind of membership, such as the chamber of lawyers or notaries. While free to choose their preferred IdPs, the AP is exclusive.
Another case is the need for attributes from multiple APs.
These use cases demonstrate the need to separate both roles, even if the default case in some areas, such as e-commerce, is more likely to be that the both roles are taken by a single entity and a single service.
There is one ambiguity left: The IdP might provide non-abstract attributes to identify the user, such as name or email address. In this case the IdP is AP as well, but this does no harm to the concept of having a separate AP.
Having said that, it might be valid to conflate both roles into the term IdP to simplify the presentation of IDM concepts, like it is done in Paypal's and InCommon glossaries.