Remove “From computer” media tab for posts with existing attachments?

To remove the From Computer tab header, you unset the type key from that array. However, this will (confusingly) not remove the tab content, and because this is the default tab it will show it even if the tab header for it is gone.

To change the default tab you must hook into the media_upload_default_tab filter. This gets called in multiple places, I did not research which one is called in which circumstances, so I moved the check for attachments to a separate function and rewrote your code like this:

add_filter('media_upload_tabs','wpse13567_media_upload_tabs', 99);
function wpse13567_media_upload_tabs( $tabs ) {
    if ( wpse13567_post_has_attachments() ) {
        unset( $tabs['type'] );
    }
    unset( $tabs['type_url'] );
    unset( $tabs['library'] );

    return $tabs;
}

add_filter( 'media_upload_default_tab', 'wpse13567_media_upload_default_tab' );
function wpse13567_media_upload_default_tab( $tab )
{
    if ( wpse13567_post_has_attachments() ) {
        return 'gallery';
    }
    return $tab;
}

function wpse13567_post_has_attachments()
{
    static $post_has_attachments = null;
    if ( null === $post_has_attachments && $post_id = (isset($_REQUEST['post_id']) ? $_REQUEST['post_id'] : false) ) {
        $post_has_attachments = count(get_posts("post_type=attachment&post_parent={$post_id}"))>0;
    }
    return $post_has_attachments;
}