Assets not being deleted automatically

I want old assets that are not in use to be deleted immediately. I've reduced the history stack by adding this to config.php: define('PERCH_UNDO_BUFFER', 1);

The assets are not marked as library assets. But after removing them from a content region, they remain visible in Assets, and the files remain in the resources folder.

This is a problem because old assets (PDFs) can continue to be accessed by website users unless they are actually deleted from the server. A Google search continues to show the old PDF in search results, the url for the old PDF is still valid and users can still access the old file. The old url will eventually drop out of Google, but this still leaves a window during which the old PDFs are accessible.

I realise I could delete the old assets manually, but this would require giving the client admin rights and it's an extra little task to do every time a new PDF is uploaded.

How can I set this up so that old assets are deleted automatically?

Here's my template - it has a repeater, with each item including a file (a restaurant menu PDF) and a thumbnail image:

<perch:before>
<ul class="menus clearfix">
</perch:before>
<perch:repeater id="menus" label="Menus">
<li><a href="<perch:content id="file" type="file" label="File" order="2" />#view=Fit"><img src="<perch:content type="image" id="thumbnail" label="Thumbnail image" order="3" width="150" height="150" crop="true" />" alt="<perch:content type="text" id="desc" />" /></a><a href="<perch:content id="file" />#view=Fit"><perch:content type="text" id="desc" label="Title" order="1" required="true" title="true" /></a></li>
</perch:repeater>
<perch:after>
</ul>
</perch:after>

Short diagnostics:

    Perch: 2.8.32, PHP: 5.5.38, MySQL: 10.0.27-MariaDB, with PDO
    Server OS: Linux, litespeed
    Installed apps: content (2.8.32), assets (2.8.32), categories (2.8.32), perch_blog (4.5.4), perch_forms (1.8.2), perch_gallery (2.8.5)
    App runtimes: <?php $apps_list = array( 'content', 'categories', 'perch_blog', 'perch_forms', 'perch_gallery' ); ?>
    PERCH_LOGINPATH: /cms
    PERCH_PATH: /home/oilyspubco/public_html/cms
    PERCH_CORE: /home/oilyspubco/public_html/cms/core
    PERCH_RESFILEPATH: /home/oilyspubco/public_html/cms/resources
    Image manipulation: GD
    PHP limits: Max upload 100M, Max POST 100M, Memory: 1024M, Total max file upload: 100M
    F1: 2edba60ed1f613d6dd804feb202456a2
    Resource folder writeable: Yes
    HTTP_HOST: oilyspub.co.uk
    DOCUMENT_ROOT: /home/oilyspubco/public_html
    REQUEST_URI: /cms/core/settings/diagnostics/
    SCRIPT_NAME: /cms/core/settings/diagnostics/index.php