It may be easier to think about each part of the job in isolation, but this results in bad practice. It does not make much sense for a part of the organization to work faster or more efficiently if it puts a strain somewhere else in the organization. One should think about how the work that each party does contributes to the overall creation of value of the organization. This way you can make decisions that benefit everyone.
No service, practice, process, department, or provider is alone. They all interact in complex ways to create value. You must think about all this every time you are deciding or planning an improvement.