Hitler's original plan was for German forces to stabilise the situation in North Africa and defend a limited area, however, Rommel went on the offensive and the rest is history.
What would you expect to change had Rommel obeyed Hitler's orders?
Well, Rommel being Rommel, he would have had a good reason to obey. That could have been a obedience inspiring “hands on” theatre commander in chief (hands on the “you’re sacked for insubordination” button that is) or a no-nonsense chief of staff.
I don’t think the campaign in North Africa would have gone any easier for the British however. Never forget that they were pretty piss poor to start and OTL needed overwhelming force to defeat 2+ ragtag German divisions at the end of a very insecure supply line. Had Rommel stayed within easy reach of Tripoli/Benghazi while the British had to rely on Tobruk (within range of Axis air power) and Cairo for their supplies, the Axis might actually have done better while defending.
The only major change would be a relocation of resources. The Germans would have considerably more motor transport assets for their Russian adventure (as Rommel got almost as much as each of the Army Groups in Russia) and less of the valuable German assets were squandered on a sideshow. If that would have been enough to make a real difference in Russia is uncertain but it would unquestionably have helped their chances of winning their “all-or-nothing 1941 invasion.
The British would not feel so threatened by an Africa Corps defending the Tripoli-Benghazi perimeter and would perhaps not allocate so much of their combat power to that theatre. Either their buildup for D-Day is accelerated as more troops are held back in England but more likely is the transfer of excess troops to the CBI (China-Burma-India) theatre. These troops will most likely be lost in the Japanese advance of late ’41 and ’42 as lack of troops was not the reason the British did poorly in the early stages of the Asian war.
I'd disagree that Rommel was thinking tactically and Hitler strategically. Rommel saw the possibilities for linking with Barbarossa if he could get through Eypt and into Iraq. Hitler couldn't see shit if you stuck his head down a toilet.
Yes I know the distances being talked about, and the reasons why supply in the desert was so difficult for the Axis but not the Allies. As per usual the solution requires Hitler to make things happen for the Axis he leads, and that wasn't going to happen, hence the eventual Allied victory in every single theatre/front without exception.
Sorry, I didn't spell my idea out at all. Hitler knew that Britian was shaping up to be an enemy from the late 30s but didn't have a coherent plan to fight them, especially after the fall of France. I'd suggest that a combination Uboat/Blitz and a Med campaign pursued straight after the Fall of France with a full 4 mobile divs. If done with enough purpose it could get Rommel to Iraq in time for the April '41 pro Axis coup, and northern Iraq isn't so far from Transcaucasia. Rommel could perhaps then strike at the SU from the south when Barbarossa was deep into the SU. The sort of political and strategic initiatives this would require is Hitlers job, I bet Churchill, Stalin or Roosevelt could string it together.