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.