It's a separation of powers idea, even in countries that don't have a formal separation of powers like in the U.S. In nearly every country, the President (or Prime Minister or King) is invested with foreign policy powers, so that the country can speak with one voice in international affairs. That power is undermined by domestic courts passing judgment on the actions of foreign sovereigns.

Nations don't have to respect each other's court judgments. On the other hand, domestic courts can decide the disposition of assets within their jurisdiction. For a country like Saudi Arabia, that has a ton of U.S. assets, a U.S. court judgment can be a big risk even if it has no intention of recognizing the validity of that judgment.