The price of oil is based on worldwide supply and demand. Increased U.S. production will not move the price of oil, How does an increase in US oil supply not affect the global price of oil? Increases or decreases in OPEC supply decrease or increase the global price. The US is significantly engaged in the global oil market, we import about as much as we produce. Increasing our domestic production decreases our draw on the global supply.
Future Asian demand and Russian supply are the big factors.
The US already produces more oil as Russia.
Expanded North American reserves would have a military value in the event of a world war that denies the U.S. access to oil beyond its shores
Reserves are not production rates. Oil in the ground does not match oil flowing to the refinery. See Venezuela for a great example.
Future incremental (increased) production, the delta, of U.S. supply and demand will be small, relative to increases in supply from countries like Russia and increases in demand from Asia. As such, increases in U.S. production will not have a significant impact on world oil prices. That should be a safe statement, without getting into a massive statistical analysis, much of it based on highly controversial data. My view is that the reason the Saudis are concerned the U.S. might become self-sufficient is more because they fear a gradual weakening the U.S. security umbrella as Persian Gulf oil becomes less important to the U.S.
You have a valid point that proven reserves of oil in bitumen form are not militarily significant, unless they are being produced. It's not just a matter of drilling some development wells. I think that military concerns are based on a remote possibility.