I agree that when looking at a business, care needs to be taken to address large (i.e. End-to-End) processes as these lead to a focus on what needs to be improved (typically Time, Cost, Quantity and Quality).
The Process Maturity Model helps business to identify strategies for moving to higher levels of maturity.
Unfortunately, business is not just about process. Attention needs to be given to other factors, such as Organisation, Products & Services, Technology, Data, Risks & Compliance, Policies, Strategy etc. What are needed are Maturity Models for these other factors. There is little point in only addressing processes, when there is a lack of clarity on risks and their controls, or data ownership is unclear. How about management of the technology used, or the products & Services Portfolios? A Business needs to address these as well.
I agree that when looking at