The price of oil is low. The cost to extract oil miles down in the Gulf of Mexico is expensive and much higher than pulling it out of the mideast sand. Therefore those extracting oil out of the Gulf are at a competitive disadvantage than those pulling it out of the sand. So just allowing more drilling by itself is not a magic wand to making us independent of foreign oil unless the exploration and production cost differentials are dealt with. We are dependent on foreign oil not just because of environmentalists.
But if the total cost of producing oil in the new Gulf of Mexico fields is $40/bbl, the cost in Middle East fields is $20/bbl and the price is $50/bbl; opening up new GoM areas will get more bidders, exploration and production for us.
The Middle East isn't exactly open to producers like it is here. Agreeing to produce oil in an OPEC country runs other risks, such as being scaled back due to OPEC production limits, just as they are forcing upon them today.
As long as there is money to be made here, we will get companies interested in producing the oil. Just because someone else has a higher profit margin, doesn't prevent expansion elsewhere.
That is why deep water and oil sands had been growing for years, even though it was cheaper in other places.