Some Miwok bows have some awesome "hooks" on the ends of the limbs, sharp recurves. The sinew and hide glue dries from the outside in. That means the outside of the sinew is going to begin to shrink before the inside starts to even think about shrinking, and this can pull the sinew up and off the recurved segments of the limb. Wrapping the sinew with cordage or other natural material prevents this from happening so that the glue/sinew interface with the wood fibers will set/harden without gapping or completely pulling off.
On the recurved tip bows I have sinewed, the last step for me has been to do sinew and hide glue wraps on the curved portions. Sometimes I leave the sinew wrapping on the belly, sometimes I have sanded it off and trusted the molecular adhesion to do what it will.
Feel free to follow cultural tradition with appropriate materials, or riff on it with modern techniques and materials as you see fit. All comes down to what pleases you and helps you achieve what you want with the particular bow.