I leave everything in the inbox and mark unread if I need to follow up. Following up may involve nothing more than a note about the task on my to-do list. I also delete a lot of useless stuff and have never regretted it.

My inbox is (1) things I need to read (2) a big searchable archive of things I might need later. Nothing more, and certainly not my to-do list. So I don't feel the need to do anything more than I'm doing.