You can shape the surfaces the way you want for the movement you need. Make them as big or small depending on how much compressive load you need to transfer. You can place as many ropes, controlled ropes or just stretch rows to have as much flexibily, control and ability to survive tension as you need.

You can do all of this with pretty crappy materials and high tolerances.

When compared to that, gears that transfer all the loads through individual small teeth that must be made from incredible materials and struggle if you need multiple degrees of freedom there's really no competition.

Unless you need to deal with fast spinning things or simple 1dof fixed axis rotations gears are terrible technology and they rarely ever evolved not because they are hard but because they have huge weeknesses and barely any advantages.

The only gears that ever evolved that I know of are used for syncing movement.