Thanks Owen! You make some very good points. I know there are some who might link to an image somewhere which they have no control over and one day, poof, its gone and they don't know until its too late. I might suggest an experience for images wherein Esri asks a simple question via a modal dialog when a user tries to upload an image. Something like:
I want to host and manage this image myself | I want ArcGIS StoryMaps to host & manage this image for me
The former would give you an input box to enter a URI. The latter would open a file select dialog and upload it to ArcGIS Online. Then, add a checkbox somewhere on the dialog to 'Remember my selection'. Left unchecked, they'll see that dialog every time they upload an image, allowing them to manage some images and let Esri manage others. Ifchecked, the user's choice is remembered and the appropriate experience is delivered based on that selection for the remainder of their session. All of these things could be managed with some simple cookies and the cookies could be invalidated whenever the user published their StoryMap or closed their tab. Just my two cents. Speaking of cents, just .10/month per (average) StoryMap is pretty good.
Anyway, there's doesn't appear to be an embed option on the cover page though. There's only two options: Add Image and Add Video. Both open a file select dialog. I don't see a way to use the Embed Widget there.