It’s not just the Bill of Rights. The entire Constitution was constructed so as to limit the power of the government.
That was one of the arguments the Founding Fathers made against having a bill of rights in the Constitution: the federal government represented the States and the People, so each one's rights were already protected. The Anti-Federalists refuted this argument by pointing to the Necessary and Proper Clause, which could read as allowing the trampling of rights if Congress thought doing so would assist it in carrying out any of its powers. The Anti-Federalists won the argument and history has proven them correct.