Some history channels promote the idea that Hitler's original plan was to use the bulk of the forces to go south (oil fields), but generals on their own went for the center and Moscow, which likely wouldn't have lead to a soviet defeat even if taken (particularly if the soviets in that scenario would still, as it played out, have moved critical industry to the Urals, where the germans couldn't possibly reach regardless).
Is this suggesting a push to the Caucuses in '41? I can't see how that's going to happen. The distances are just enormous and would blow apart the Nazi's already fragile logistics. And I'm pretty sure even they knew that. There definitely were incidences of Nazi commanders pushing towards Moscow without orders from Hitler, such as immediately after Smolensk, but as far as I know, they were trying to preempt the turn south into Ukraine to defeat the Soviet forces there, which was then to be followed by an attack towards Moscow (i.e. what happened) rather than a full on push into the Caucuses.
And it's worth noting that, while it's a common suggestion, attacking straight towards Moscow after Smolensk wouldn't have helped. You're putting battered units at the end of a supply line about 250 miles further from their railheads that the historic Operation Typhoon with the best part of a million hostile troops on the flank of your salient....
Had they put 10% of the effort they put into Barbarossa into north Africa they could have taken the middle east from the UK and had all the oil they needed.
Maybe it wasn't possible to land that many more troops in italian Africa?
Would it be viable if they occupied parts of Turkey and reached the Caucasus from there? (though, again, they'd need to at least control the Hellespond, which might be doable with mines, though?)
And, it's logistics again. Putting 10% of the effort of Barbarossa into North Africa just isn't practical. By the time the Nazi's reach Egypt, their supply lines across the desert are horribly overstretched - they weren't even close to keeping the historical Afrika Korps supplied, and that's with a disproportionate amount of logistical support compared to the size of force. They could certainly do better with more trucks, but not practically to a level which would matter. And that's before you get to the Italian Merchant Marine shipping all this through a contested sea. Meanwhile, Britain can easily ship in men and supplies from India and, on the defensive in Egypt, have very short land based lines. Without Barbarossa, I don't see Britain being able to take the offensive in North Africa, but for the Nazi's to defeat them, at least in the short term, is a pretty big stretch.
The success of both Operation Compass and the Afrika Korps prior to El-Alamein 1 were due to catching unprepared enemies on the bounce and looting supplies, and there's a big difference between that and fighting a prepared foe while having to bring in your supplies over a thousand miles of desert.
As for Turkey, taking the European parts, and even crossing the Bosphorus will be pretty easy. But then you run into Anatolia and the L-word. Keeping a modern (for the time) motorised army supplied across 1940s Anatolia is again a nightmare.
Of course, I probably should've pointed this out in my last post, but while invading the Soviet Union was a huge mistake for the Nazis, it was also inevitable for the Nazis. The destruction of Communism, the acquisition of Lebensraum and the enslavement of the Slavic race were fundamental ideological principles for them. You get rid of those, and we're in the territory of "Notzi". And at that point, you've probably butterflied away the whole war, let alone Barbarossa....