Question

What was a purpose for establishing missions in the New World?

Answer 1

The best option would be to teach and train Native Americans. 

It is known since the very beginning that people are incredibly unruly. People make terrible decisions not thinking if this could mess up other people's lives. As long as it gives them convenience, other people's welfare does not matter to them.   
As a result, the government establishes a mission that could be used to clean things up- a mission for the New World. Its mere purpose is to teach and train the Natives. 
The Natives emphasized here are the uncivilized ones, those who have not known and have not acquired the power of a highly civilized conscious being.

They believe that only through teaching and training the minds of these people we can attain peace and order. 

And once this goal is achieved, growing new crops and protecting settlers and traders would no longer be a problem. People will now help each other progress. No more selfishness. Abundance is all over and sharing is everywhere. 

Answer 2

The purpose for establishing missions in the New World was that it wanted to teach and train Native Americans. The first Christian baptisms in the New World took place in the island of Hispaniola. This also want to tech the Native Americans on other livelihood.