Wrapping a cord around your arm causing problems is actually an old wive's tale from the person not properly twisting the cord in the process. With every wrap around your elbow, you need to rotate the free-end of the cord accordingly.
If you know how to coil a rigid air hose without that hose laying in a mess, then you know how to properly wrap a power cord. The problem is, is that most people don't know this because the power cord is flexible enough to not force you to do it.
With every wrap around your elbow, you twist the free-end of the cord 1 revolution. The result is no different than putting the cord on a rotary reel. Yes, I used to be in the business, and yes, I would laugh at the guys wrapping figure-8's. It was messy, and it meant that they didn't understand the process of wrapping a cord.
If you do it right, you should be able to coil a cord or hose flat on the ground (no elbow or guide), and it will follow a tight circle without any loops wanting to stand off the ground. If any loop stands off the ground, it means you have not twisted it from its normal lay.
This guy shows it fairly well with a small extension cord.