Any Hostname not disabling domain on WP settings page

That is actually a design design, to prevent users from accidentally changing the site_url and home_url settings into temporary, private or otherwise publicly inaccessible domain names. Also, should you change those setting and then deactivate the plugin your sites actual URL would have changed without that being your intention.

Since Any Hostname tries to alter all URLs accessed by visitors this should not be an issue, as it is only displayed to admins. Or perhaps I am not understanding your problem correctly?