What is one reason why the united states elects presidential candidates indirectly through delegates rather than by popular vote?

One reason for that is a historical reason: at the time when the system was set up, there was no mass communication yet, so organizing a big election would have been almost impossible. 

Instead, it was decided, that each state would choose their delegates ( who would presumably ask around and find out what people of their states want) and only those delegates would come to the  capital. I was cheaper and possible to do, as asking all the citizens would not have been possible within any reasonable time constraints.