Yes, that's all true. But a new government here in the USA is going to look pretty much exactly like the current one, because this is the government the voters want.
Republics only work well when the voters are smart enough to make decent choices. Our citizens are so uneducated and lacking in critical thought that they can't do this.
In my opinion, the best thing the USA could do to have fewer problems and have a government that more closely follows the will of the people is for it to break up into smaller countries. Large countries don't work well as republics; they're too big and diverse, and no one can agree on anything. Notice how Europeans don't complain too much about their governments; it's because people in France don't have to come up with agreements on every little thing with people from Italy, Germany, or Kosovo (such as the headscarves/burqa issue that's in the news lately); they live separately, and only cooperate on monetary policy and trade. We should be more like Europe: separate into smaller countries or regions (like northwest, southwest, southeast, northeast, and midwest), and then only have an economic union like the EU so we can share a currency and have free trade between the members. Then, the people in the southeast and southwest can have lax gun laws while the people in the northeast can ban them all, some parts can have lots of welfare and high taxes while other parts have less welfare and lower taxes, some parts have no regulation of banks and have mortgage meltdowns while other parts have more regulation and a steadier economy, etc.