Assuming you're using SimpleMachinesForum software, a forum admin should be able to disable the ability to post attachments.
Admin -> Members Submenu -> Permissions
Navigate to the group you want to change, then Modify.
Toward the bottom, there will be a submenu about Attachments.
If you want this for every group, there's a faster way via Advanced Settings, at the bottom of the Permissions Groups List.
Select all the groups, then scroll to the bottom, use the last row to "Clear Permission" - Post Attachments
It might help to make this a software enforced situation, at least to help with people who don't read (like me)