FWIW, my system is:
-immediately open all mail. Discard junk. Anything that's just for filing goes into the filing pile. Anything I need to deal with gets put into the desk.
-Each weekend, I grab my checkbook and anything I need to deal with from the desk, pay bills, balance as needed, etc. If something needs dealing with during business hours, it junks up my little table by the couch so I remember to get to it.
-I divert a lot of paper from coming in by switching most bills to online only.
The desk is usually a mess, but it closes so you can't see the mess. The filing pile tends to sit until I feel like dealing with it, I need to get into the files, or am moving the file box for cleaning. Whichever comes first.