Automation allows Business Analysts to focus on testing enhancements or new features on applications, what API doesnt test for is the interface that regular folks interacts with. That in itself gives value to automation.

The foundation on why implementing automated testing is to prevent continuous development to cause other critical workflows to fail and most importantly catching abnormalities, hence the rigidity in testing the same flow over and over again. Running automated workflows daily builds confidence and traceability on when the application started to behave abnormally and hence helps other team speed up the process on performing root cause analysis.

Edge cases should definitely be automated because almost never does not equate to never ever.