Recent project had good reason to move from a document library to a custom list, but still needed to require attachments.
Here is how to do that. Original solution found here: https://social.technet.microsoft.com/Forums/sharepoint/en-US/c93d7611-f634-4c03-ae0d-3b5ecfe5ca6a/how-to-make-attachment-required-field
I had to perform the insert in SharePoint Designer, but the idea is the same.
To help my customer I also added a view to show them if items did not have attachments, it was as simple as creating a view with a filter of Attachments equal to No.