We'll create fresh WordPress site with Random Auto Featured Image installed. You have 20 minutes to test the plugin after that site we'll be deleted.
For posts with no featured image, and no images associated with the post, a random image is selected from the media library and set as the featured image.
The plugin currently does not test for images associated with the post.
Instead, install and run the Easy Add Thumbnail plugin (https://wordpress.org/plugins/easy-add-thumbnail/).
That plugin will set the featured image on all posts that both have no featured image AND have an image associated with the post.
What is left is posts without featured images and without any images.
This plugin provides a random image from the sites media library so that index pages look more interesting (and possibly confusing/humorous depending on which image is randomly selected.)
There is a notice at the bottom of each post the plugin has updated noting the random image. In a future release, this note will be optional via the standard user interface, but for now one has to edit the plugin and remove the last “filter” line.