Unsetting post_tag taxonomy breaks term description for other taxonomies

Try using this function to avoid your problem:

function sld_unregister_taxonomy_from_object_type($taxonomy, $object_type) { 
        global $wp_taxonomies;  
        if ( !isset($wp_taxonomies[$taxonomy]) || !get_post_type_object($object_type) ) return false; 
        foreach (array_keys($wp_taxonomies[$taxonomy]->object_type) as $array_key) { 
                if ($wp_taxonomies[$taxonomy]->object_type[$array_key] == $array_key) { 
                        unset ($wp_taxonomies[$taxonomy]->object_type[$array_key]); 
                        return true; 
                } 
        } 
        return false; 
}

e.x.:

function mwm_unregister_taxonomy(){

    sld_unregister_taxonomy_from_object_type( 'post_tag', 'post' );

}

add_action( 'init', 'mwm_unregister_taxonomy');