The problem is the idea that a single elected official can somehow represent the entire United States. Can one person understand and represent 300 million people?

Impossible.

At least, impossible on a deep level. Such understanding is possible only in a very general level, for issues that are very broad.

Therefore, government should be as small, localized, and focused as possible. As much power as possible should be invested at the local level.

A lot of Europeans don't get this. European countries are already small and homogeneous (apologies for a huge generalization). They already have a fairly local government. The USA needs to work differently because it's the third most populous country in the world and because it's so enormously diverse. Government should be as close to the people as possible. Then if you don't like your municipality or state, you can move a few miles away to get a different municipal / state government.

I'm much more concerned about electing people whom I've met personally and had the chance to interact with at a town hall. Grass roots movements are much more effective at understanding people in a deep way. From a conservative perspective (my perspective), the Tea Party is a movement that has had great success enforcing accountability and toppling incumbents. There are similar movements in other political camps as well.

Here's the point: localized government increases freedom and choice. It puts local government in a position where it has to compete with other governments (municipal or state). That kind of competition can potentially squeeze out corruption and increase accountability.