We had this argument not so long ago.
First and foremost, you don't have barrett m82 or some other modern sniper rifle (BM gets a gun) but a bow and arrows. So your contr-argument is invalid.
Secondly even if you run with it, nothing stops you from pulling a trigger, if you are close enough you may even score a hit from hip.
Also nothing stops bowman from pulling string and aiming while running, you don't have a scope anyway. So older mastery was better in terms of "reality". You can still fire an arrow when moving, it just won't hit for so much. Not only that, it was also closer to reality where not only damage is lower while moving but also range becomes worse (since its harder to hit something while moving).
Modern sniping with rifle and sniping with a bow is something completely different:
https://youtu.be/BEG-ly9tQGk?t=177
https://youtu.be/BEG-ly9tQGk?t=255