There's also a philosophical reason for the adoption of an indirect, representative democracy. One specific example is to protect against Tyranny of the Majority [1].
I'm dubious that a country where most issues are voted on directly by the people could function with any significant amount of participation, mostly because people are not experts in most fields, and don't necessarily understand e.g. the macroeconomic effects of letting the largest banks in the world all go bankrupt. We elect representatives because there is a lot of work to do governing a country thousands of miles wide with over 300 million people, and I want people who can devote their profession to improving government in charge. Ones that we get to vote for regularly, of course.
[1] https://en.wikipedia.org/wiki/Tyranny_of_the_majority
"Second. It is of great importance in a republic not only to guard the society against the oppression of its rulers, but to guard one part of the society against the injustice of the other part. Different interests necessarily exist in different classes of citizens. If a majority be united by a common interest, the rights of the minority will be insecure. "
- James Madison, Federalist #51 : http://www.constitution.org/fed/federa51.htm