There is a curious ambiguity about the word "iteration". Sometimes it means doing exactly the same thing, over and over again; sometimes it means doing something slightly different each time.
When a process is drawn as a loop, we need to understand what exactly this means. Which aspects of the process are the same for each execution of the process, and which aspects are different? What is the nature of the feedback, allowing each iteration to improve on previous iterations, and what is the scope for learning and development?
For example, a business process architecture may include a product development cycle. We usually understand this to mean not that the products themselves are recycled, but that there is some accumulation of knowledge and experience (trial and error, learning by doing) that allows each product and each product-related activity to learn from and improve upon previous iterations.
Therefore a process model that is drawn as a loop or cycle cannot be interpreted in the same way as a process model that is drawn as a simple production line or value chain, because there is something else important going on. This is one of the reasons I distinguish the Cybernetic View (which specifically looks at feedback and its effects) from the Activity View (which looks at the work itself). The Cybernetic View allows the architect to pay attention to the effectiveness and efficiency of the feedback, which is not the same thing as the effectiveness and efficiency of the underlying activities but is at a different logical level.
One process that is attracting a lot of interest at the moment is the commissioning process. Commissioning is an important component of a healthcare system, and I also heard Jennifer Saunders recently talking about commissioning at the BBC. I wanted to see how people were depicting the commissioning process, so I did an internet search for images associated with the term "commissioning". The top six diagrams (ignoring one diagram that wasn't really about commissioning but about paying commission) all showed commissioning as some kind of cycle.
This selection of diagrams reflects a common agreement that commissioning can be thought of as a cycle. However, although the wide variety of diagram styles might be regarded as merely a fashion statement, it could be a sign of a more fundamental methodological issue. It is not clear that all these sources share the same understanding of what it means for commissioning to be regarded as a cycle. What do these diagrams tell us about how the commissioning process develops and evolves and hopefully improves over time? Are there different categories of improvement, with different cycle times?
There is also the question of responsibility. Are the same people responsible for both executing and improving the commissioning process, or does improvement call for a different kind of distributed intelligence?
So there are lots of important and interesting questions here, which a traditional process model doesn't help much with.