I believe this CAN be done quite easily in the existing reporting tool, although it is not intuitive because the option does not reside in the due date menu, but is given as a task status option as a filter. Here’s how I did it:
Go to Reporting, add a new chart
Select template: Incomplete Tasks by Project
Click add filter, select Task Status then select Unscheduled
Add other filters as required (e.g. you probably want to filter out complete tasks)
Rename Chart to Tasks with no Due Date
You will now have a chart which shows, by project, how many tasks do not have a due date entered allowing you to find these tasks and enter a date