The US has though exploited plenty of oil from the Middle East. US and British oil companies were among the first to organise, and the two governments had no compunction about kicking any opposition to the curb. So though we might see little oil flowing this direction now, it's not always been that way. And, a stated purpose for US engagement in the ME since at least the Carter administration, is the free uninterrupted flow of oil from the region.
This is what happened in the early 1950s in Iran. The Iranian government, under Prime Minister Mohammad Mossadeq, nationalized Iran's oil in 1951. Iran's concession was unusual for the Middle East in that there was only one parent company, BP. When its holdings were nationalized, BP obtained court orders enjoining other companies from buying oil from the Iranian government. Afraid of the example that a successful nationali- zation might set for other Middle Eastern oil exporting states,
the British and American governments worked to destabilize and eventually to overthrow the Mossadeq regime. The restoration of the Shah in 1953 following a brief period of ouster also reinstated foreign oil companies as managers of the nationalized Iranian oil company.
http://www.globaloilwatch.com/reports/political-economy-middle-eastern-oil-tetreault.pdf