llamas are definitely herd animals
Slings are used to herd them even today.
Yaks too, and alpacas etc.
Any animals that man has domesticated is a herd animal.
One of the points, is that the original interior indians probably were also herders - so no reason they wouldn't have slings. It's my understanding that very little is known about them.
I would consider 1500 to be modern history
The documentary I saw indicated that the interior indians did not survive long after europaen contact with the americas. There were also a lot of indications that coastal indians had abandoned settlements en-masse to move into the interior in the same time period.
Pretty much the only advantage a sling has over a bow is distance and easy to make ammunition.
For many cultures the disadvantages outweigh those.
Much longer learning curve than a bow, not as good for hunting larger animals, and lack of stealth when stalking.
A bow can be held cocked, ready to fire for an extended period - a sling can't.
YOu pretty much have to stand up and make a large movement that will alert your prey. Bows can be used from a semi prone position quite easily.
Slings would be superior for hunting waterfowl as you can launch several missiles at once - much like a shotgun.
And you are primarily shooting at animals that have been spooked already.