I think the part I keep forgetting is the "Menu" mouse button. In the RISC OS case, having the application icon in the Icon Bar is, effectively, like having the application "foreground and running." A "Menu"-click on the icon parallels having, say, a MacOS 7.5 application running with its menu visible at the top of the screen. The Mac puts it more "in your face" but either way the ability to open the application menu and start a new document is essentially equivalent in both cases.
I'm reminded of the utility !Menon that I used to keep track of all my important files across many floppies, once upon a time. No window at all IIRC. Just drag and drop, and the Menu button.