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Properly managed projects will assign tasks to every available resource. Project managers don't just assign tasks, they also assign deadlines. Deadlines, unfortunately, are a necessary evil. There's always one or two employees who don't need them, but for the rest of us, deadlines are motivating in and of themselves. Deadlines get things done.
Another reason that project management leads to more productivity is that there is no ambiguity when it comes to what a particular resource should be doing at any given time. This means there is less time for employees to spend hem-hawing over what might need to be done or slacking because they believe they have nothing to do. With clearly defined milestones, deliverables and objectives, there is no room for ambiguity within project management.
There are also a lot of checks in project management. Between resource analysis, the project plan, constant reporting and monitoring from the team and project manager, there are very few surprises in a properly managed project. The project manager will be well-aware when a project is slipping behind schedule, when an important deliverable is missing or when someone has become overwhelmed through overallocation.