btw if rope starts off non-twisty and develops twist, the twists are being put into it.
I can't think how twists will happen in use as a kite halyard (I might be wrong) so it must happen when it is coiled for storage. Since my climbing days I never coil ropes by 'winding' them over my arm, like I used to - halve it, halve it again and again, and again etc then put an overhand or figure 8 into the (whole) coil to hold it together.
With very long or large diameter ropes you halve it, then drape it over your neck and flake, then flake, then flake...try doing it over a 1,000m drop

You can quite easily remove twists from rope by using your hand to 'run them' to the end of the rope - takes a bit of patience but it works. It also works on telephone handset wires but this is getting scary....must have been my potty training.