You are absolutely 100% wrong about this. It is entirely possible in the US to enter into contracts that limit your rights, including freedom of speech. People do this routinely, and it is enforceable.
The reason you can't give away your kidney in an employment contract is because there is a specific law banning that: the National Organ Transplant Act of 1984, which bans transferring a human organ in exchange for valuable consideration.
The reason you can't give away your kidney in an employment contract is because there is a specific law banning that: the National Organ Transplant Act of 1984, which bans transferring a human organ in exchange for valuable consideration.