How is there no backlash? I can’t imagine a rope drive without backlash.
The advantage over gears is that overloads are distributed over much more material. You don't snap gear teeth. This is good for leg landing shocks.
[1] https://www.impact-fibers.com/info/unveiling-the-strength-ke...
Steel cables would work just as well if weight isn't a consideration, but I think Dyneema is likely to be more resistant to abrasion. However, heat produced by any significant dynamic friction will ruin it immediately, as I found to my sorrow. Kevlar is much more heat-resistant, and of course steel is more heat-resistant than Kevlar.
I'm quite fond of bowstring as a material for this sort of thing. It usually has other fibres mixed in with it so it's a little more bouncy than raw dyneema but that's minimised if you get thread that's intended for crossbows. It's usually waxed so there's some friction to it when you're manipulating it, and it's also easy to source.