Spot on speech from OP. There is a specific procedure to handle priority tagged luggages, all baggage handlers are obliged to follow it. Presuming that "important" means pax with "priority" luggage tags. Other issue is their baggage handling. During the last year, the baggage handlers succeded to break my luggage two times. The second time were LH flights with connection in MUC and FRA to overseas, the bag had HON tag(as F pax) on it. Someone made a hole to that luggage bag in one of those airports. Unfortunately I did not noticed it at the airport and therefore did not placed a claim afterwards. Fortunately the bag was still under the warranty and the official brand repair store fixed it.