The reserve holds about 714 million barrels.
The USA uses about 19 million barres per day.
714/19 = 36 day supply of oil the US.
Further more the oil in the reserve needs to be pumped out, refined and moved to fueling stations.
Perhaps is fair to say the the strategic oil reserve helped keep gas below $10 per gallon but not below $7
So now imagine what's going to happen when that is turned off, and even worse when the oil market sees pressure from the US buying millions and millions of barrels to take them off the market and throw them back into the reserve...
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.