Traditions in software testing suggest that the balance among the various types of test types (Acceptance, API, Integration, Unit) should be weighted toward the lower-level, more granular tests and less toward the larger-scale, or end-to-end tests. The visualization is typically something along these lines, in terms of the effort that should be devoted to each:
You know the history well. At an executive level, the organization has decided to "go Agile". Everyone in the organization attended a 1/2 day Scrum Training course. The project managers were re-titled as "Scrum Masters" and the business analysts were re-labeled "Product Owners". Finally, the developers and testers were reorganized into a set of Scrum Teams and "Sprint Zero" was started. Since that time, the teams have been "Scrumming".
A business leader approached my colleague and complained, "I invested $50 million last year in new testing environments for Continuous Integration - It was a waste, we are hardly getting any benefit from it." How is it that an organization could establish a solid beginning for CI, investing in the environments, tooling and test automation and yet get little benefit. Sadly, we've seen this movie play out so many times that we know exactly what didn't happen in the organization.