One thing to keep in mind when talking about different fibres is that the handling and treatment during processing and then the construction has as much or usually more to do with the end product as the chemistry/characteristics of the raw material.
There are lots of tradeoffs to be made when manufacturing twine. Short staple fibres (cotton, sisal etc) need quite a lot of twist to mechanically lock the fibres together. This twist then needs to be balanced by twining two or more strands or else the construction will be unstable. Adding twist also makes for desnser, more "wiry" string, which may kink. Since lots of what is easily available is designed as "utility" cord, ease of handling is often given a higher impotance than ulitmate strength.
Synthetics are a whoel different problem since what we see as consumers is usually filament (continuous strands making up the yarn) spun. In this case, ultimate strength (and lowest stretch) is highest when the filaments are most parallel (no twist) Some twist can be added to keep the whole mess manageable, or it can be braided. Now almost all the sythetics are stronger than we really need to start with, but this "strong" config has horrible abrasion resistance. Poor long term strength too, as losing one strand essentially takes it out of the picture for the whole length. Mechanically locking the strands togetherby twisting or braiding dramatically increases the wear resistance. The cord may get "fuzzy" but it will take some beating before it wears through.
Ooof. All that said, hemp _should_ be a nice sling fibre, though I suspect that the stuff that they sell for necklaces etc is
designed to get ratty looking
. Jute can be quite nice if you find good stuff. Mos of what is sold as sisal these days is pretty poor, but you might get lucky.
Wool would be good if you can find worsted type yarn (not fluffly mitten stuff). Needs to be plyed/cableds/braided.
Any of the synthetics should be good if you want to go this route. If you are keen, you'll gain by starting with the smallest diameter you can find and plying or braiding tightly to get up to the size you want.
The trick of course is _finding_ any of this stuff. In today's everything-prepackaged, precooked, preassembled etc world people aren't expected to _need_ string.