I think Thomas Berger points to an area in which BIBFRAME could potentially make an improvement on existing resource description practices.
As was said, the statement of responsibility is intended to reflect how a resource represents itself, without imposing rigorous normalization. This serves a purpose for users (although maybe not, as Thomas points out), but it also (primarily?) serves a purpose for catalogers when they make authority records for the entities involved in the creation of a work.
This can fairly be straightforward, as in the case of "Der Zauberberg / by Th[omas] Mann," but it can become quite complex in instances of multiple authorship or multiple roles (as is the case in film and theater productions, for example). So, for a feature film, we might have (from http://bibframe.org/resources/BUx1406479872/
<bf:titleStatement>El corazón del bosque / una película de Arándano, S.A. ; producida por Luis Megino ; guión, Manuel Gutiérrez Aragón y Luis Megino ; dirección, Manuel Gutiérrez Aragón.</bf:titleStatement>
Catalogers talk about "establishing" a name based on "usage." The statement of responsibility provides evidence that catalogers can point to as justification when choosing the "authorized" form of a name. In a name authority record, differing usages are cited as variant access points (as shown in Thomas's example authority record for Mao). Further, in RDA authority records, role terms (such as "una película de," "producida," or "guión," above) can be cited as evidence for establishing an entity's occupation or area of activity, which might be additionally helpful for disambiguation purposes.
In its current form (in both MARC and BIBFRAME), the statement of responsibility serves to provide human-readable information that can then be interpreted by catalogers and encoded in authority records. Of course, this is a very string-based approach. Still, the basic intention of establishing a preferred form of a name (the way an entity would seem to prefer to be known in publication) does seem valid as a resource description practice.
However, if this information could be structured up-front (as Thomas suggests), we might have a basis for the automatic generation of preferred and variant name forms in authority records (or even the automatic generation of new authority records).
Now, BIBFRAME already has a Title Entity class, and I think the validity of this construct has been debated here because it was seen as a simple "translation" from MARC encoding.
Wouldn't it be more useful to create something like a Responsibility Entity class in BIBFRAME? This would not be a replication of MARC encoding, but would provide the ability to structure data in new ways.
So, we might split up the statement of responsibility for each creator/contributor:
and then link to Responsibility resources that could be structured accordingly:
The hypothetical bf:isUsageFor property could link to the bf:Authority for the organization in question:
Although this would add a layer of complexity, maybe it would be worth it?