In the administration part of JIRA it is possible to enable/disable the ability to create unassigned issues. This is now done globally and therefore affects all projects, but it should be possible to do this on a project level.

This could be extended further so it actually resembles the global permissions vs. the project specific permissions, so that every global option also could be decided on a project level (Allow users to vote on issues, Allow users to watch issues, Allow Attachments, Allow unassigned issues, etc).

– Thomas Watson