That's less a lie and more 'teaching the ideal.' The problem isn't learning how the system is supposed to work. That's how you learn to be a mechanic. You learn how an engine is supposed to work so you can spot where it's gone wrong. The issue is more one of there are millions of people and they get 10 minutes on how it's supposed to work and then only 3 of them go into politics and learn how it actually works/doesn't work. Democracy requires more than a one week chapter on civics, once a year. We all have to be mechanics, or at least be prepared to try.

I think it can be fixed

I mean, good luck. The Principle-Agent Problem is a classic of sociology, particularly with respect to business. If you can solve it, there's a Nobel in Economics waiting for you.

Democracy is an attempt at aligning in the interests of the plurality principles with their government agencies. But there's obviously a whole lot of flaws with democracy generally speaking, even before you get into the particulars of the American system.

I do think that the Lockean Social Contract, as the foundation for any governmental system, is a more interesting and more well-thought-out concept to explore than the mythology surrounding the American three-branch system. Chomsky's Manufacturing Consent does an excellent job of breaking down how a public body can be turned against its own interests. Zinn's People's History gives a ton of insight into the underbelly of the American political beast and how people respond to industrial and state oppression. State and Revolution does an excellent job of describing the role of the state in society and how it can best be dismantled.

But the endless debate around whether US Government works as described or intended really loses the forest of social economy for the ideological tent post trees. Fetishization of the US system only contributes to its rot and our own downfall.