'You represent your state first. Then you represent the United States of America ."
Ummm, I think a little civics lesson is in order. The only people in the entire country that represent a state are the 100 US Senators. The US Congressional Representatives represent their districts, and state legislators and senators represent their districts. That's how representative government works in this country. If the legislators at every level don't do the bidding of the people that elected them, they are betraying their trust and of course that results in them getting voted out of office. Most people really like their legislators because they do such a good job representing them, which is why hardly any incumbents ever face a serious challenge at the ballot box.
An issue that you don't address is the fact the our politicians, as awful as they may be, put everything else in their life aside to run for public office, and stepped up to do the fucking job. There isn't some magical underground group of people who would do any better who are just waiting for their chance. Every single problem with our politicians has been present in democracies since Ancient Greece.