If the wound involves a body cavity, the patient will continue to bleed internally even if you stick a tampon in the bullet hole. If it is an extremity wound, you run the risk of converting a partial arterial or venous injury into a complete transection, which can be more difficult to repair. External pressure, either by direct pressure or tourniquet if you have one, is the way to go. There really isn't anything you can do to stop bleeding in the chest or abdominal cavities unless you are in an OR.
Packing is sometimes used in an OR to stop otherwise uncontrollable bleeding, usually either in the pelvis or liver. But that is done with the abdomen open, and after other measures to control bleeding have failed. It is part of the "damage control" approach sometimes used in critically ill patients, where what you are trying to do is stop immediate bleeding, resuscitate/transfuse the patient, correct the inevitable coagulopathy that occurs with massive blood loss, and then plan to return to the OR usually within 24 hrs for definitive repair. That is totally acceptable in that situation but doesn't apply to what we are talking here, ie, dealing with injuries in the field.
On a historical note, I did hear people talk of using tampons back in the late 80s still, but it had already gone by the wayside at that point.