Arcgis Online doesn't provide the export map option in its map viewers (advanced and classic). However, there's a web app builder way in which you can print it, but it doesn't incorporate the changes done in advanced map viewer (such as blending of layers, symbolizations exclusive to the advanced version only). The whole point of introducing an advanced version of web map viewer gets jeopardized here itself.
I feel the interface can be made much more friendly for the users, with this simple addition of print feature in the map viewers.
This is a big issue itself, as most of the professionals need the maps to be used in documentations and presentation purpose out of this arcgis online domain. I don't know if this is purposely being done by the developers to restrict the benefits of the service, but do you really think this will stop people from taking snapshots and getting the job done somehow.
I do not agree with what you indicate, since personally I see Arcgis Online as a complement to the desktop application.
However, I understand that a kind of printing model can be defined so that these can be output in pdf and jpg in a personalized way.
This control can be done in appbuilder from the print widget, the problem I have is that I still cannot get that configuration to go out by default.