Hi Jeremy,
Unfortunately, there's not a way for incidents to be unassigned completely. However, a work around that you might find useful is to
create a group (you could even call it "unassigned" if you wanted) and make this group
the default owner for customer created incidents.
This could function as a normal group, and you could then run reports for that group to pull up the currently unassigned to a technician incidents.
Please let me know if that helps or if you need any further information on how to accomplish this and thank you for using Service Desk!