For a brief period, Kevlar was being used for parachute suspension lines. It was found to not be dimensionally stable and parachutes using it were going out of trim fairly quickly. It was also more subject to degradation from grit and sweat than Spectra or Dacron was and loses its strength faster than others when exposed to sunlight.

I have a set I use occasionally, but the Kevlar lines are very draggy compared to the SS. You wouldn't want to use'em on a plane that tended to be light on the lines to begin with. The extra drag might compensate for a plane that tended to slew to the outside too much that didn't have adjustable leadouts.

They won't get kinked in a weedy field. That's one advantage.