Because they had an alternative: the atlatl. It is a dart thrower, made from a narrow piece of wood usualy the length of a forearm with a 'hook' on one end and some form of grip on the ither (some have leather loops, some have shaped the wood to easily hold it). By extending the length of the arm it bettered the distance and speed a dart could be thrown. In my experimental archaeology class my professor told me that during a tryout on the efectiveness of the weapon a dart went straigt through a car door. So basically they did not need the bow. There are pros and cons to each: and atlatl is much faster to make, and if you need to wait for a long time you could keep it ready to throw with minimal effort, needs only one hand and is particularly adapted for large open spaces. The bow is much easier to use on forested areas, has a greater accuracy range (though often lesser strenght upon impact) and can be used while moving. For further reading i recommend Hutchings and Bruchert's article Spear Thrower Performance: ethnographic and experimental research and Zelia Nuttal's The Atlatl or Spear Thrower of the Ancient Mexicans (this is an older piece but Zelia is the mother of mexican archaeology and i love her)

This is a good question, and my knowledge of the era and location is very very surface-level, but didn't ancient middle/south-american cultures use other projectile weapons like javelins and the like?