Media image edit isn't saving changed image and remove the existing image

Core Media module with Image bundle configured at /admin/structure/media/manage/image :
* Do not "Create new revision" (not sure if this is required)
* "Field mapping" set some fields to be mapped from the image field (e.g. Name, MIME Type, File Size).

Steps to reproduce
1. Add a new media image.
2. Edit the media image, remove the image file and upload a new one. Save the form.
3. The media library now shows a "broken image" icon. If you try to edit again, the new image file is gone. If you inspect with Devel, the image field is now empty.