You can punch through even very good armour at point-blank ranges with a decent composite bow and suitable arrows, but the circumstances allowing for such activity were rare outside naval engagements and sieges.
First of all most of your points are perfectly fine. But from what I have read even an arrow from pointblank range from a heavy warbow has little chance to do any harm to the protected areas of mail-armored soldier. The difficulties are mainly in getting a wellmade and historical piece of armor shot under the right conditions.

I personally find it most interesting that Plutarch in the Life of Crassus first says (24, P389):

4 And when Crassus ordered his light-armed troops to make a charge, they did not advance far, but encountering a multitude of arrows, abandoned their undertaking and ran back for shelter among the men-at‑arms, among whom they caused the beginning of disorder and fear, for these now saw the velocity and force of the arrows, which fractured armour, and tore their way through every covering alike, whether hard or soft.

5 But the Parthians now stood at long intervals from one another and began to shoot their arrows from all sides at once, not with any accurate aim (for the dense formation of the Romans would not suffer an archer to miss even if he wished it), but making vigorous and powerful shots from bows which were large and mighty and curved so as to discharge their missiles with great force.

6 At once, then, the plight of the Romans was a grievous one; for if they kept their ranks, they were wounded in great numbers, and if they tried to come to close quarters with the enemy, they were just as far from effecting anything and suffered just as much. For the Parthians shot as they fled, and next to the Scythians, they do this most effectively; and it is a very clever thing to seek safety while still fighting, and to take away the shame of flight.
An interesting part about the Parthian tactic:

25 Now as long as they had hopes that the enemy would exhaust their missiles and desist from battle or fight at close quarters, the Romans held out; but when they perceived that many camels laden with arrows were at hand, from which the Parthians who first encircled them took a fresh supply, then Crassus, seeing no end to this, began to lose heart, and sent messengers to his son with orders to force an engagement with the enemy before he was surrounded; for it was his wing especially which the enemy were attacking and surrounding with their cavalry, in the hope of getting in his rear.

2 Accordingly, the young man took thirteen hundred horsemen, of whom a thousand had come from Caesar, five hundred archers, and eight cohorts of the men-at‑arms who were nearest him, and led them all to the charge. But the Parthians who were trying to envelop him, either because, as some say, they encountered marshes, or because they were manoeuvring to attack Publius as far as possible from his father, wheeled about and made off.

3 Then Publius, shouting that the men did not stand their ground, rode after them, and with him Censorinus and Megabacchus, the latter distinguished for his courage and strength, Censorinus a man of senatorial dignity and a powerful speaker, and both of them comrades of Publius and nearly of the same age. The cavalry followed after Publius, and even the infantry kept pace with them in the zeal and joy which their hopes inspired; for they thought they were victorious and in pursuit of the enemy, until, after they had gone forward a long distance, they perceived the ruse. For the seeming fugitives wheeled about and were joined at the same time by others more numerous still.

4 Then the Romans halted, supposing that the enemy would come to close quarters with them, since they were so few in number. But the Parthians stationed their mail-clad horsemen in front of the Romans, and then with the rest of their cavalry in loose array rode round them, tearing up the surface of the ground, and raising from the depths great heaps of sand which fell in limitless showers of dust, so that the Romans could neither see clearly nor speak plainly,
Now it gets very interesting,

5 but, being crowded into a narrow compass and falling upon one another, were shot, and died no easy nor even speedy death. For, in the agonies of convulsive pain, and writhing about the arrows, they would break them off in their wounds, and then in trying to pull out by force the barbed heads which had pierced their veins and sinews, they tore and disfigured themselves the more.
The barbed heads were usually larger, with three blades (triloblate?), and not well suited to pierce mail. It seems from the description that the large mass was wounded through shots in the arms and legs - or in the case of the lightly armored troops in the body.


Thus many died, and the survivors also were incapacitated for fighting. And when Publius urged them to charge the enemy's mail-clad horsemen, they showed him that their hands were riveted to their shields and their feet nailed through and through to the ground, so that they were helpless either for flight or for self-defence.
The survivors - the majority were mostly wounded in the extremities.
9 But the Gauls were distressed above all things by the heat and their thirst, to both of which they were unused; and most of their horses had perished by being driven against the long spears. They were therefore compelled to retire upon the men-at‑arms, taking with them Publius, who was severely wounded. And seeing a sandy hillock near by, they all retired to it, and fastened their horses in the centre; then locking their shields together on the outside, they thought they could more easily defend themselves against the Barbarians. 10 But it turned out just the other way. For on level ground, the front ranks do, to some extent, afford relief to those who are behind them. But here, where the inequality of the ground raised one man above another, and lifted every man who was behind another into greater prominence, there was no such thing as escape, but they were all alike hit with arrows, bewailing their inglorious and ineffectual death.

11 Now there were with Publius two Greeks, of those who dwelt near by in Carrhae, Hieronymus and Nicomachus. These joined in trying to persuade him to slip away with them and make their escape to Ichnae, a city which had espoused the Roman cause and was not far off. But Publius, declaring that no death could have such terrors for him as to make him desert those who were perishing on his account, ordered them to save their own lives, bade them farewell, and p397dismissed them. Then he himself, being unable to use his hand, which had been pierced through with an arrow, presented his side to his shield-bearer and ordered him to strike home with his sword.
Once again an important - and well armored person is wounded where the armor doesn't protect him. Usually it is the eye but here the hand of him is pierced.

27 Even as he spoke such words of encouragement, Crassus saw that not many of his men listened with any eagerness, but when he also bade them raise the battle cry, he discovered how despondent his army was, so weak, feeble, and uneven was the shout they made, while that which came from the Barbarians was clear and bold. Then, as the enemy got to work, their light cavalry rode round on the flanks of the Romans and shot them with arrows, while the mail-clad horsemen in front, plying their long spears, kept driving them together into a narrow space, except those who, to escape death from the arrows, made bold to rush desperately upon their foes. 2 These did little damage, but met with a speedy death from great and fatal wounds, since the spear which the Parthians thrust into the horses was heavy with steel, and often had impetus enough to pierce through two men at once. After fighting in this manner till night came on, the Parthians withdrew, saying that they would grant Crassus one night in which to bewail his son, unless, with a better regard for his own interests, he should consent to go to Arsaces instead of being carried there.
This is an important passus about the power of their spears - seemingly a topos to explain the defeat of the Romans, like the power of the "unknown" parthian composite bow.

http://penelope.uchicago.edu/Thayer/...assus*.html#23

Cheers
OA