I have observed that when people are informed they are not productive, the natural tendency is for them to take on more tasks almost as if they felt by showing they could complete a lot more tasks, they will be seen as productive team members. In a way, they are right. Productive people do complete tasks. However, they do NOT try to do everything. It may seem counterintuitive but sometimes the best way to become more productive is to do less. An Accountant doesn’t try to design the company website by themselves. They know that is not the most productive use of their time and skills.
The project that your team doesn’t take on, doesn’t have to be completed by you. Perhaps, your team does not have the capacity to deliver on that project. In which case, it is better to pass on it and focus on projects that play to your strengths.
What about all the tasks you do. Are there any that could be done better by someone else? If you have the authority, you should delegate as many tasks as possible. If you are not in a position to delegate but can make a convincing case for why someone else should be doing a task you have been assigned, talk to your boss. The most productive people focus on a few core areas where they can deliver the best results and rely on others to do what they can not.
Not all problems need to be solved by you. There is a very compelling reason why rich people outsource tasks like laundry and cooking. It can be done better by a Professional and it frees them to focus on tasks that bring in even more money. Think about that when next you decide to take on a task.