>>> Why are they curly in the first place
For the same reason that most landline phone handset cables are. So that they will be long enough to stretch to where you want them but, at the same time, won't be hanging down on the floor when the device is in its 'stored' position.
I've never had a problem untangling a phone's curly handset cord by simply holding the 'phone end' of the cord up high and letting the weight of the handset untwist the cord. Have you tried holding the 'other' end of the cable up high and letting the remote control hang down (possibly pulling down from the top of the cord with your fingers as you do so)? I'd normally expect that to be all that's need to get rid of the tangles.