Re: “What good does it do to export oil if it keeps the supply down and the prices up in the US?”
Sorry, I disagree.
When the USA exports oil, it just means that the specific oil in a specific geographic location can be exported at a higher price (most likely to Europe) than it can be sold in the USA.
The oil we import - mostly from Mexico and western Canada - is cheaper than the oil we export, primarily because of transportation costs and proximity to local USA markets.
There are a lot more promising areas to drill and frack too. If our production keeps rising at 12-15% per year, we are going to be able to meet all of our own needs in just a few years.