Alexander in Kevlar....

[bobbin]

Because the shape of the arrowhead is designed so that if you try to pull it out the way it came in you could end up causing far more damage and risk the head coming off. Such a method would only have been used if the thing was really deep (and the victim was relatively unimportant) or in a limb.

Also leaving it in would be very dangerous as any movement could lead to further injury, most couldn't wait until after the battle.