Anybody who has ever been in a serious snowball fight knows the power of the two snowball technique, a high lob to distract followed by a quick fastball (to the face/torso). An army of professional archers would undoubtedly be experts in the same technique.
A unit of archers has a very limited supply of arrows, enough to shoot for a few minutes before they have to resupply. They also cannot precise aim a lobbed shot because their weapons do not have the appropriate sight nor a rifled barrel to maintain accuracy or energy with a high lob. Arrows fired in an excessively high arc are wasted.
It seems like your intuition of weapons and warfare comes from mass media, not historical evidence or practitioners.
We have skeletal evidence of professional archers. It takes years of dedicated practice since adolescence in order to modify the bone structure like that. That additional bone strength means these professionals were likely able to use draw strengths no modern enthusiast could even touch. It also follows that if they were part of a standing army, they also undoubtedly practiced skills together and used a variety of equipment, like short bows and longbows.
Unfortunately, we have no mass media that reflects what a professional archer of yesteryear looked like because that profession died centuries ago and nobody has modified their skeleton to amuse us. However, we can tell from some of their bones they were somewhat lopsided as the arms were conditioned for purpose. For example:
"The men of the Towton population appear to have been engaged in a habitual activity that preferentially loaded the left humerus when compared with the right. This disparity is strongest in the distal humeral shaft. The loading pattern varies such that it creates significant differences between limbs in diaphyseal shape from the mid-distal to midproximal shaft." [0]
Despite what the weekend warriors and LARPers would like to believe, the historical professionals really were anatomically and physically better at the job.
What does draw strength have to do with not having an computed sight for hitting a moving target with a top-down shot, or the lack if rifling to keep an arrow from tumbling when gravity slows it down at the top of the required ballistic curve? Or the scarcity of ammunition? These are issues if technology, not of training or exercise.
Who needs sights or rifling? Just like any professional athlete, thousands and thousands of practice shots (eg, 10,000 hours) to develop muscle memory is all it takes to become proficient.*
Maybe go to a LARP or reanectment event and participate (arrows with rubber endings) to compare if there are differences with your close range snowball fight.
"army of professional archers would undoubtedly be experts in the same technique."
Because I do doubt that a lot. There is no one shooting in the air on a battlefield to distract.
To answer below:
My fellow Sunday Leaguers also study and re-enact Champions League football. It's a lot of fun but I'm not foolish enough to think I belong on the pitch in a real competition. I didn't train my whole life to be an expert footballer and most researchers didn't train their whole life to drive an arrow through a man in battle.
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And there are still native tribes doing hunting and warfare with bows, that were and are studied. And some reenactment freaks are in a way better shape than their ancestors ever were, due to heavy training and better food.
Nobody is shooting in the air with an arrow to distract like you would a snowball. You shoot straight.
Hm. Are you aware that reenactment and research often go hand in hand? And if those people won't know, who actually try it out - then sureley you would know better. But how?
Dangerous arrows tend to come from the same general direction. If the archer is close enough to shoot straight, arrows coming from above have so little energy that they are mostly harmless. If the archer had shot them with enough energy to penetrate armor, they would land behind you.
Or, you can protect your front while the arrows get dropped on your head. Decisions, decisions...