This method of construction was used because it was very difficult to cast a solid barrel and then drill it out without the bit coming out the side.
Damascus barrels were generally designed for black powder charges. The breech end of the tube was much thicker than the muzzle end, and this held the initial impulse pressure from the black powder. By the time the bullet reached the muzzle, the pressure had dropped quite a bit, so muzzle reinforcement wasn't needed. This gave a better weight distribution through the length of the weapon.
Smokeless powders burn more slowly than black powder, but maintain high pressures throughout the barrel. Since the barrel is not reinforced at the muzzle, it may not be able to contain the pressure. Also, most Damascus barrels were made before modern smokeless powders, so the age of the barrel can be a safety hazard.