After an animal dies, the blood coagulates pretty quickly. Also, if an animal is strangled, then drained of blood, you will not get nearly as much blood out by gravity alone (even if the animal is hung upside down). Very much of it will still remain in the veins/arteries and especially the capillaries.
I would thing the worst thing about strangulation would be that it causes blood vessels to pop and deposits blood into the meat/tissues (like petechiae)... (and I also wonder if eating bruised/injured parts of an animal would be similar).
When you cut a major artery (like the carotid/jugular), the heart continues to pump until all the blood is removed and the animal is truly exsanguinated.
I don't know all of these things for a fact as pertaining to The Bible or the necessary way to slaughter animals for food. Honestly, this is the first time I ever recall hearing abut it. These are just a couple things that came to mind on why it makes sense to me that the animal be exsanguinated and especially not strangled, given that we are not to eat/drink the blood (since the life of flesh is in the blood).
Honestly (to me), this is just one of many 100s (if not 1000s) of scientific facts we find in The Bible. There are countless things in The Bible that weren't understood in ancient (or even recent) times that we understand now, because of modern science and technology.
(page 6 explains petechiae and the spilling of blood into the tissues from strangulation). If I'm not mistaken there are injuries from strangulation that are worse and deposit a lot more blood into the tissues than petechiae. It shouldn't be too difficult to find information or sources if anyone's interested.
When it comes to petechiae, contusions (bruising), hemorrhages and other forms of injuries from strangulation it becomes impossible to remove all the blood from an animal. The same goes for animals that are already dead.The blood quickly starts to thicken and in short time it becomes impossible to remove all the blood (especially from capillaries and tissues). Not even modern technology (like pumps) could remove it all.