For reports that are not calendars there isn't any need to copy the report. Have your system admin allow you to have manage rights to those reports, and then make sure you run a report to make sure none of them are run with the rights of the exiting owner (if they are, you'll have to pick someone else).
For reports that ARE calendars, best practice would be to use the service account to own those. This way if you leave, your successor doesn't have to copy those for the second or third time, and so on.