Gallery not working without id's

I have a gallery on a WordPress page on a site that I’ve taken over. The author explicitly wrote out the id’s of the images he wanted to display:

[gallery ids="87,185,186,188"]

The (non-techy) person for whom the site was made would like to be able to add and remove images easily. Finding the image ID and inserting it into the list is not easy for them. What would be easy would be if I could have them use the Media Library as the ‘editor’ for which images show up and which don’t. So what I did was change the code to the following:

[gallery]

Which I thought would display all the images uploaded to that page (of which there are four, as explicitly listed above). Instead, it displays nothing.

The documentation for the gallery shortcode seems to say that [gallery] should just work. Is this not the standard behavior? How would I troubleshoot this?