I monitor my gps position 24/7 with gpslogger. Does it really have to be there always? I'd like to remove it completely, I know that it's on. Wifi spots show my location anyway and the green dot does not show up when an app requests wifi data.
You may make the green dot as a normal icon in the statusbar showing that gps is running. Maybe with a gps pin symbol instead of a green dot? I think I remember that I already had phones in the past that did this.