How do I permanently Disable Attachment Post URL

The form for the ‘From Url’ tab seems to be pretty much hard-coded, so I don’t think there is away of removing the ‘Link Image To’ field.

However, for the Media Library tab you can remove the link field, with the following:

add_filter('attachment_fields_to_edit', 'my_attachment_fields_edit', 10, 2);
function my_attachment_fields_edit($form_fields,$post){ 
    //Set attachment link to none and hide it.
    $html = "<input type="hidden" name="attachments[".$post->ID."][url]" value=""/>";

    $form_fields['url']['html'] = $html; //Replace html
    $form_fields['url']['label'] = ''; //Remove label
    $form_fields['url']['helps'] ='';//Remove help text

    return $form_fields;
}