One of the aims of shechita is to drain blood but it’s not the sole purpose of the practice. The legal literature even states that if an animal mysteriously releases no blood during slaughter the meat is still considered kosher. Although it must undergo salting to be eaten raw, something not normally required.
When an animal is shechted the heart quickly pumps the blood out of the body regardless of what position it’s in. This myth likely partially originates from the practice of hanging certain animals upside down during shechita. But this method of animal restraint, known as shackle and hoist, only gained prevalence because of USDA regulation and not kosher law. Additionally shackle and hoist is rarely practiced in the U.S. today.