I will be carrying a separate bag for odds and ends as well as one or two film cameras plus film. Putting the Zoom F4 in that same bag, might be the best option. As with all things, more thought needed.
Update* Thought of some other advantages to bagging the recorder.
1) It will be less of a distraction for the people I am shooting, especially the children. If the kids see all those flashing lights there figures will be all over the recorder to play with the dials. When we become friends the children's fingers tend to fly over my camera camera gear, children are so curious and love to try to do stuff and see how things work. I might be better off hiding this unit away.
2) If I fall into the garbage as happens occasionally I would have some protection (cloth bag) between the garbage and my sound gear.
Update** Been playing with a bag for the Zoom F4 Audio Field Recorder tonight. I think this is the way I will got, it makes my rig look less intimidating, it provides protection for my audio recorder and as bonus I will have a space to hang my earphones and film cameras (1or2 35mms, Leica rangefinder or SLR and 1 120mm, a Plaubel Makina or Rollieflex).