That's not a good way to make an argument. Other factors (Chinese demand, speculation, etc.) might keep driving prices up even when production increases, but that doesn't mean, at all, that increased production is innocuous.
As I said, even if you discount the effect on prices (and you can't), each extra gallon the US produces is one less gallon it imports, and you do have a monstrous trade deficit. Surely you can't dispute this.
Trade balance is definitely a factor. But for the other, the reason I use the shorthand of my previous post is that just because a theory says something, even though the real world is not in compliance with the theory, does not mean that we are required to assume that the theory is correct.
We have had strong growth in domestic US supply, primarily through improvements in technology making previously uneconomic oil and gas deposits commercially viable. And yet there was a huge surge in oil prices. And that was at a time when US refineries were at a relatively low utilization capacity.
Clearly supply alone is not driving prices at the pump.
Studies have shown Wall St speculation is adding about $0.50/gallon to the retail price. But further than that, you have to understand that oil is not a free market on the global scale. It is heavily concentrated in few producers who can, and routinely do, manipulate the market for their own interests. And so the point is that there is no foreseeable change in US domestic production that can be expected to have other than trivial price effects. And the why of that is very simple. Saudi Arabia and some of the other OPEC producers can make themselves better off by managing production quantities to offset US production improvements. And because they can, and because it is a profit maximizing strategy both in the short and the long run, that is what they do.
But even Saudi Arabia isn't able to fully manipulate prices. In 2008 when prices were spiking SA could not sell all the oil it was willing to produce to push the prices down. And that is because the refinery level of the business is oligarchically controlled as well.
So saying drill baby drill, and expecting that to have any significant effect on near or even medium term prices is not going to work.
Further, you have to remember that oil is somewhat price elastic. While supply is managed to keep prices in a range, if price falls demand rises. And so that offsets the advantages of drilling.
So really nearly the entire benefit to the US is in terms of the trade deficit. There are some jobs, but oil production doesn't employ really large numbers of people. So drilling isn't "bad" for the US, but it is also not more than a fairly minor "good" for the country.