Proper dressing of the wound include:

-direct pressure and dressing
-elevate
-dressing
-pressure point
-tourniquet

None of the dressings I came in contact with in the field had any hard plastic in them (except for soft one). I don't think that plastic part would cause any type of damage to the tissue underneath if would was reassessed in the reasonable time. Discomfort maybe but damage very unlikely. Also it shouldn’t be placed directly over the wound since that would prevent absorption of blood and forming of scab. But if you think about it there can be couple of different scenarios to it. If you using such bandage to work over a laceration on the arm and when wrapping it up the plastic part ends up over brachial artery. Automatically that would slow (or stop) down blood flow to rest of your arm. That can be potentially dangerous. Such bandage would definitely be more dangerous to kids since they are more sensitive to lack of oxygen. Also if area of injury has a potential to swell and you have a plastic there that will not stretch or adjust this is another pressure point that may cut of blood supply. I think that when using Army type of medical supplies (I'm assuming you are talking about Israeli Army bandage) you have to remember that those things are designed to treat gunshots, amputations and battlefield injuries, not household type of emergencies. It is acceptable for the military to have certain amount of casualties while it is totally unacceptable in civilian life. But in conclusion I think it’s all about placement of the hard plastic tab and proper follow up care and checking on your interventions.

Matt