There's a workaround on Android that comes to mind. The "Share" plugin can be used to show the share tray on Android, allowing a user to choose an app to use a image with. A quick test showed that you can use this to save to photos, upload to twitter etc.
The downside being that Safari only supports sharing text and URL at the moment, not files. You could encode the image as a data URI and share that instead but the user would only be able to post this to social media and the like, not download the image.