Never, ever, take off the band, or as you refer to it, the label. When a master blender creates a cigar blend, he determines just how far you are to smoke it, in order to properly experience what he has created. The factory applies the band, at the exact point you are suppose to stop smoking. Going beyond this point is disrespectful to the creator of the blend.
The cello, or what you refer to as plastic, must be left on the cigar at all times. It is bio-degradable, and will slowly dissolve over time. The blender determines just how long he wants the cigar to age, and instructs the factory to cover his creation, in a cello wrapper of just the right thickness required to accomplish this. Once the cello wrapper has fully dissolved, the cigar is ready to smoke. This is why you must maintain proper humidity, because if the humidity is too low, the cello will not dissolve in a timely manor, and you'll end up with an overaged cigar. When you see a cigar without cello, it means that is ready, and needs to be smoked right away. Smoking a cigar before the cello has dissolved, is an insult to the creator of the blend.