Actually the United States has an “oral law” system. It is very flexible. The ‘Common law”, like Halakah evolves by scholars and judges addressing situations as they change. The Romans had a written system reliant on the boss making rules whenever he felt like. If you tried to reinact living as we did 2000 years ago you would realize how are flexible oral system, like the American common law system, works in our benefit.
If you followed the original text of the Constitution and Bill of Rights, as an example, gun ownership would be dependent on willingness to serve in the militia and report regularly for training (and to fight war, and more often, suppress riots). The clear understanding when the Constitution was adopted was that non-Christians would have minimal rights under state law unless the state wanted them to (by the Jacksonian era, they all had). None of the civil rights that enable American Jews to be comfortably middle class would exist if the Constitution was interpreted as it was in 1789 (of the14th amendment at the time it was adopted).