Like I said, if you make the figure 8 loops you are making two twists in opposite directions for each loop. When you uncoil the rope, the twists cancels out each other and you hopefully have a length of line without twists. Folding the line dont introduce twist at all into the line.
Both my crew and I used do do a lot of rock and mountain climbing. Getting twist into the lines while climbing is outright dangerous, so the climbing community have developed ways to avoid that. Always folding the rope is the best way to avoid twists, barring putting the line into a rope-bag. We consequently always fold lines on our boat, and lock up the folded lines by doing some turns around the hoop and a a self-locking hitch. Quick, easy and relatively idiot-proof. Try it, and compare handling with figure-8 coils. The true test is coiling and uncoiling twin trapeze lines. If you can do that without twists and snarls you have a good method.

While talking about coiling and twists. When storing the SS rigging, we dont coil the wires but roll them up. When rigging the mast/boat, we dont uncoil the wires, but unroll them. This is another variation on the same problem, how to avoid twist and kinks.