I agree, but not just the oil companies.
Most of the major transnationals should be broken up into smaller entities.
Not necessarily because we need more "players" (although that would be a side benefit)
but because the current set of "players" exert undue influence over government policies, rigging the system to their own advantage and to the detriment of the American People.
"Merchants have no country. The mere spot they stand on does not constitute so strong an attachment as that from which they draw their gains."
--Thomas Jefferson to Horatio G. Spafford, 1814. ME 14:119
"I hope we shall... crush in its birth the aristocracy of our moneyed corporations, which dare already to challenge our government to a trial of strength and bid defiance to the laws of our country."
--Thomas Jefferson to George Logan, 1816. FE 10:69
"Fascism should more appropriately be called corporatism because it is a merger of state and corporate power."
-- Benito Mussolini
On the contrary, the only solution that will get good results is less regulation and more competition. The reason the companies must be behemoths to survive is because of the costs, risks, regulations, lobbying costs and political risks associated with this industry. With less governmental interference there will be more competition and lower prices for the consumer.