Though there were many factors involved overall, there was a primary reason Germany didn't focus all their forces on the Caucasus region during Operation Barbarosa. That reason was the German leadership's unflinching confidence that the Russians would be defeated by Nazi forces in a single summer campaign.
That is, by the end of summer the plan called for a Soviet surrender, and going into fall 90 divisions of the German military would be left operational as an occupational force in the Soviet Union. All other German Military forces were to be re-deployed or drawn down.
Not only was this the Nazi plan, the following source gives one an idea what other military powers thought of the German invasion as they became aware:
(From Chapter 1, page 3, "The World Will hold Its Breath") As of June 23, 1942 -- In Washington, the War Department War Plans Division expected a Soviet defeat in one to three months. Robert E. Sherwood, Roosevelt and Hopkins (New York: Harper, 1950, p. 303). Sir Stafford Cripps, the British ambassador in Moscow, predicted a German victory in three to four weeks, while the British Joint Intelligence Committee gave the Russians "a few months at the outside." (J. M. A. Gwyer, Grand Strategy London: Her Majesty's Stationery Office, 1964, vol. III, pt. I, p. 90.) Indeed, BARBAROSSA appeared to be, as Hitler claimed, the greatest military operation of all time, capable of defeating the Soviet Union in a single summer's campaign.
In short, both Hitler and his most powerful enemies--outside of Moscow--were certain that not only would the Nazis defeat the Soviet Union but that they would do so with relative ease.
This being the case, Hitler and The German High Command expected to win the oil fields of the Caucasus and their production facilities still intact, as they would have been in use right up until the surrender. In addition, he expected to rid Germany of this enemy for good.
If Hitler and the others had been correct, Germany would have won the war and basically, made money while doing it.