We are always used to read about which standards influence supplier quality but not often we read about the feedback from this department and its importance in the company.
Wether your Supplier Quality Department is driven by purchasing (focused on strategic sourcing) or driven by Quality (focused in standarisation); the relation between quality, purchasing, engineering, among other departments and supplier quality is not questionable.
Supplier simple solutions on small plant problems can lead to a catalogue on Continuous improvements. Benchmarking your Suppliers in simple quality daily problems is always profitable. Ask sometimes your supplier quality or involve them in brainstorming, you will be surprised on their know how.
With reference to purchasing, who is the first person (along with the purchaser) to visit a supplier ? Think about also your initial visit audits, from social corporate to environmental, logistics, etc.. Your supplier quality has a global overview of the company. This ends up in commodity knowledge. So, If your supplier Quality is an expert, your purchasing should be always asking for advice in case of new technologies, which supplier is more convenient and so on.
Finally for engineering, there is one word: Feasibility. In all companies I have been, or when I even was a Supplier Quality Engineer, we had something to say about tolerances and specifications. We can positively feedback about all questions technically related.
As a conclusion, all I am trying to say is that the reasons why your supplier quality should be often considered in internal discussions is not only as a feedback on supplier base but also as a way of benchmarking and learning of technologies, standards and best practices.