Users in an an organization should be able to host and share graphical assets to be used as symbols, icons, banners, photos, or any type that is a png, jpg, etc. You might sat we can now (as of 4/2015 ) - technically we can, but it is both technically broken for some cases and is also not the best workflow from a usabilty standpoint. The two cases I would suggest addressing first are those for images to be used as organizational symbols and images to be used as the photo images in storymaps. The other cases - group icons, banners, etc, work well now, but these also would fall into this new improved workflow.
There needs to be an new asset type for images, of which a user picks whether it is a symbol, photo, or icon, and the corresponging user interfaces across the site, whether for users or admins, respond appropriately and list those organizational graphical assets. These items would not appear in the gallery and would be able to be browsed on their own in a new section of the organizational site. Admins could enforce file size limits and dimensions on images for storymaps and whether symbols must be transparent.
Why the current workflow is broken for image hosting: We can post images as items to ArcGIS Online today but this workflow doesn't technically work since the image must be shared with 'everyone' to be used as a symbol in a map. If everyone sharing is disabled the url doesnt present for accessing the image, and one must put it on dropbox or another 3rd party location. The current workflow of sharing images on ArcGIS Online to be used as resources is also a poor use of that feature since the images appear as items in the organizations gallery and one must enter metadata. Also, if the images are symbols, there isn't a good way to realize they even exist when authoring a map. They don't appear in the symbology authoring GUI. These are the reasons why we need a new workflow for images on ArcGIS Online for map symbols.
Story Maps also benefit: In addition, images can also be used within storymaps as art assets, ie. photos. Users should be able to contribute to this library of graphical assets. This would enable assets to be controlled and not put on the open internet when used in an organizational story map, and remove the need for third party image hosting.