If I'm not mistaken, isn't that the role of the Supreme Court?
Actually, no. It is a role that the court assumed for itself in Marbury v. Madison, but nowhere is that power enumerated in the Constitution. The Founders envisioned a Court system to settle disputes between the states and also provided not for 3 co-equal branches, but for a Legislature that would be the more powerful branch, with a reasonably strong executive branch as a partial check and with a judiciary that was subservient to the Congress, since Congress can decide what matters fall under its jurisdiction as per Article 3, Section 2, Clause 2: In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
If I'm not mistaken, isn't that the role of the Supreme Court?
Not entirely. The US Constitution is a contract between the Federal Government and the various State Governments. To be meaningful there must be a balancing force which works on behalf of the states.