Additionally, the US did not stop the exports of oil though any federal trade policy when prices went from ~2 - $7 per gallon. Exports continued at a in the ~3,500 barrels per day.
https://www.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=pet&s=w...
In 2021 imports were slightly higher the exports: https://www.eia.gov/tools/faqs/faq.php?id=727&t=6#:~:text=Cr....
In short, another tool the fed could use to lower prices would be to ban or reduce exports of US oil when prices are high.