Why do you think horse archers have stirrups???
It is to stand up and pull heavy bows and arrows to deliver deadly shots.
There you have it! They can do more than 180degrees…
You don’t have any knowledge of how horse archers use their body and develps muscle.
Horse archers back in the time especially the Mongol ones had stirrups to allow them to stand up and pull heavier bows. Today people just do this for fun and keep their tradition.
Back in the time, it was meant to kill.
About the bow
You cannot compare European bows to Asian Composite Recurve bows as the Composite Recurve bow will perform 1.5x times better than any European bows.
Historically, European foot archers were not able to hit the Mongol horse archers from afar due to low range, but the Mongol horse archers were able to kill them with ease.
How do you think the Mongols were able to fight against European Knights using horse archers and turn it into a massacre, not battle? The horse archers’ main target is not the rider, but the horse. Taking out the horse would have a 70% chance to kill the rider as it could drop on the man who is mounted on it and stirrups caused the main issue. So the Mongols simply shot the horses and it killed its rider no matter the armour they have, plate, lamellar, etc.