From 1975 to 2015 the US had a law banning most crude oil exports from the US (aside from Canada and partially Mexico), effectively creating a separate North America-only oil market. It wouldn't take much for the US to reinstate this ban, meaning oil produced in the US stays in the US. And since the US is a net oil exporter, that means North American oil prices will stay low and stable.
That is irrelevant. Oil is fungible. Block oil exports from the Middle East and the price of oil skyrockets worldwide including in the US.