The exsanguination is necessary to enable some types of delicate reconstructive surgery where bleeding would obscure the working area.
A bloodless area is also required to introduce local anaesthetic agents for a regional nerve block.
[1] The original version was designed by Friedrich von Esmarch, professor of surgery at the University of Kiel, Germany, and is generally used in battlefield medicine.
A pink looking variant of this medical tool was issued out to Soviet Infantry as early as the Soviet–Afghan War.
There are many pictures of the Esmarch bandage, during the Afghanistan and Russian-Chechen Wars, being used to aid with the comfort of the stock, or a supposed attempt to make it more easily accessible.