In movies archery volleys over walls and other obstacles are regularly depicted as fairly effective, especially if the archers have ample arrows for repeat volleys.
Even if only of sporadic value, it was certainly a benefit in war unavailable to gunpowder weapons until after 1500. https://en.wikipedia.org/wiki/Mortar_(weapon)
Trebuchets and similar weapons had the same capacity, but they were large scale siege weapons, primarily. How effective in combat were archery volleys against hidden concentrations of troops?
A quotation from The First Crusade by August C. Krey, in reference to a rout during the Peasants' Crusade where the remains of the Christian force fled to an old fortress near Constantinople:
"Above the shore of the sea was an ancient deserted fortress toward which three thousand pilgrims rushed in flight- They entered it in hope of defense, but, finding no gate, they piled up their shields and a huge mound of rocks in the doorway and bravely defended themselves with lances, wooden bows, and sling stones. But the Turks surrounded the fortress, which was without a roof, and aimed their arrows so high that they fell from the air in a shower and struck the enclosed Christians, killing the poor wretches."
The practice of shooting arrows at high angles is supported in Arab Archery in the form of "zone shooting", a stunt shot that emphasises high angles:
The first of these is zone shooting (ramy al-dārāt) which is most telling against enemies. It consists of drawing a circle on the ground and then going away from it the distance of the cast of the bow, from which position you shoot upward, high into the air, toward the circle. When the arrow falls it should alight in the circle. You should practice this until you master it, say from a distance of one hundred cubits. You then come up twenty cubits nearer to the circle and again practice shooting up into the sky and having the arrow alight in the circle. Once you master the cast from that distance, you again come up twenty cubits closer and shoot again in the same way. You should continue your practice from successive points, each twenty cubits closer, until you can drop your arrow into the circle in that fashion from a distance of twenty cubits. If you can do that successfully, you shall have mastered the art of zone shooting: one of the most useful in storming towers and fortifications, where no other type of shooting would avail. In this way the arrows descend upon the enemy from above like crashing thunder while they are unaware. This will inflict great losses upon the enemy and will enable the Moslems to storm their strongholds successfully. Records show that a certain eastern city was stormed and occupied in this fashion.
While not a siege, the use of high-angled volleys was a turning point in the Battle of Hastings in 1066, in which the Normans under William the Conqueror nullified the effectiveness of the Anglo-Saxon shield wall by forcing the defenders to raise their shields, breaking the integrity of the wall. King Harold Godwinsson was struck in the eye by an arrow and killed.
It would be safe to say, based on sources describing archery and archery aiming methods, that high-angle long-distance shooting was an integral part of archery training.