Birds pull apart the single strands of pieces of rope or string. When the strings get caught around legs, toes, necks, or any other part of the bird, the bird will likely flap wildly to try to get out of it, which of course causes the string to wrap even more tightly. The result can be lost limbs or death. We know of one Amazon who ate a piece of string, which caused her vent area to prolapse, and since she was also carrying an egg, she wasn't able to pass it, and she died. We don't recommend toys made solely or mostly of rope because it's too easy for a bird to get toes, etc. caught in them.
Long toenails are particularly prone to getting caught in rope.
A very popular element of toys and birds love it. Just be sure your birds' toenails are trimmed enough to avoid their getting them stuck inside pieces of leather. Also be sure that any leather you allow your bird to play with is untreated . Again, they are accidents waiting to happen. The above scenarios aren't automatically going to happen to your birds, but they are dangers.