The governance that often comes with a traditional waterfall project management environment can reduce opportunity for critical thought and personal accountability. Project Managers are often held to strict methodology guidelines and monitored relentlessly to make sure they are completing every step. They in turn assign tasks to the project team members and monitor the tasks with little thought as to the relationship of the task to the goal. This strict governance leads to a Project Manager modifying reality to fit the plan rather than responding to change.
Agile Manifesto value: Responding to change over following a plan
No matter the methodology, the person that is physically doing the work should be treated as a professional and asked to identify the work to be done in the form of tasks/checklists, estimate the cost/duration of their tasks, and be accountable to their tasks. Project Managers should address roadblocks, handle change requests, and support the people doing the work. Providing an environment that motivates individuals through transparent communication, shared ownership, and trust will maximize results in any environment.