Admins to have Delete access to all private reports.
Maybe, a better enhancement will be adding a "Reports" section to the Admin Console, where you can edit permissions, edit the report, delete it - or just having the option to delete that report.
I can understand you when you say "deleting private reports" without a permission is a bad solution, because me saying "Admin" - in the eyes of a developer - is just a role. And a role doesn't have a special flag in the metadb, it's just what you control it to be via the Admin Console.
BUT - having that section in the console - I think that would solve it.
We really got tired from asking people if they're using a, or some reports, or if they can delete their draft and find out they're not in today or this week. Most of the time we receive a reply that "......not using it anymore, you can definitely delete it" - and find we don't have permission to do so, again - as admins only.
We do sometimes have a procedure to batch-delete everything that is not being used for the last 3 months or more, but it would be great if we could delete things when we need to.