We're not using the recent items functionality of the application menu and want to hide the whole area. Can this be done?
While technically you could probably remove/collapse that from the ApplicationMenu's template, the right side of the ApplicationMenu is a requirement of the Office UI Guidelines and exclusion would be a violation of the license you have from MS to use the Ribbon UI. Also, menus in the left hand side are positioned & sized based on the size of the right hand side since the ui guidelines require that the menu occlude the right hand side.
Makes sense, thanks for the explanation.