I assume the main point is that they can be moved by a heavy duty forklift with a single fork pole through the center of the roll. As anyone who’s tried to roll a barrel knows, having to stop regularly and re-aim the roll, or turn corners, is no fun; moreso when you’re talking thousands of pounds. Plus, how would you push something like that? And stop it? Loaded from the side by a forklift explains why they are oriented as they are.
It’s far more common to use an overhead crane with a flat hook but the reason is the same. The tools used for loading and unloading will approach from the side. There are some good photos here:
Also, whatever happens to the coil before and after the truck part is probably done horizontally: slitting, stamping, coating, plating, etc.
Also, the coil can be secured with chains through the center of the roll, thus ensuring that they will not go anywhere unless the chain breaks - not slipping sideways, or the chains slipping off the roll.
Obviously, including cradles would be even more secure, but as previously mentioned, there’s the handling of the cradles too. Also, if you can’t trust multiple chains and anchors, then the problem isn’t the cylindrical shape.