I use dual coax for our ground tripod. I have had no problem keeping the cables in coils about 12" by rolling in the cable without twisting it. It d0es get to be a little challenge with the 100' pieces. I use both arms like a reel.
Is it critical to not twist the cable, no, but it looks better and outs less stress on the cables. Once twisting starts, it grows.
I only buy solid copper core coax.
I only use a windup reel with single coax cables.