In effect, the U.S. has been doing both. Fourteen of the 18 Iraqi provinces have effectively been oil-spotted; there is no insurgent activity to speak of in them. In the remaining four, the locus of action is being pushed out of the populated areas into the mostly empty desert west of Ar Ramadi.
The key to a successful oil spot strategy is to have Iraqi security forces of sufficient size and competence to be able to hold and clear areas (like Fallujah) from which insurgents (largely) have been driven. This process got off to a woefully slow start, but has been going gangbusters since LtGen. David Petreaus took over responsibility for training the ISF a year ago last Spring. But it takes time. It will be late next Spring at the earliest before sufficient numbers of trained Iraqi soldiers and cops are on hand to make an oil spot to be truly effective.
In the meantime, U.S. troops have been for months transitioning into precisely the role Krepinevich advocates. U.S. advisers are being embedded with Iraqi units; Iraqi companies are being attached to American battalions, and plans are being made to consolidate U.S. forces in four mega-bases around the country, with dozens of bases we're currently using being turned over, gradually, to the Iraqis.
Krepinevich deprecates both the importance of and the success in building an Iraqi democracy, which I think is a huge mistake on his part.
It's amazing to me how many people who ought to know better take the mostly erroneous, wildly pessimistic view of the situation in Iraq presented by the MSM as if it were Gospel.