Gen.Mannerheim
Grand Moff
All that getting involved in North Africa really did was put the already precarious Nazi logistic and supply abilities under additional stress. If controlling the Mediterranean was as important as you say, the Nazis made horrendous blunders by deciding to invade the Soviet Union. (Never mind that the Nazis were on the verge of bankruptcy to the Soviet Union and in desperation was selling them battleships and fully formed industrial plants capable of making synthetic rubber.)
The Axis was monstrously unable to properly fight a prolonged campaign in the Mediterranean. The Germans has just short of zero naval presence in the area. While the Italian navy was a significant force, they were mainly designed to compete with the French and sunk most of the r&d into odd advancements (like extremely high muzzle velocity for their main guns) and not the more practical areas (like night fighting). As a result, the Regia Marina had a poor record against the Royal Navy. Thus any campaign in North Africa would see large amounts of arms and material never make it to their intended ports, and leaving the Axis on a poor footing.
Finally it was a success
Was it though? Besides partially knocking Italy out of the Axis Powers and taking Rome, the Italian Campaign didn't accomplish its goal of hastening the end of the war. The allies didn't even break into Northern Italy until early 1945. It bogged down large numbers of Allied troops, many of which were siphoned off to other fronts in mid-late 1944.
I think the criticism that's usually made against Montgomery was on a personal level among other commanders in the field.
Montgomery is right alongside MacArthur in being some of the worst commanders in terms of understanding/willing to work in an Alliance/Coalition system. Both were quick to claim subordinate successes as their own while also quickly shifting blame for setbacks on allied forces. While MacArthur should have been shot for treason (his high level of esteem still held in American culture is frustrating), Monty was just openly disobedient to his superiors. Monty thought his plans were superior simply because they were his plans. This is confirmed from memoirs from his subordinates. For example, even if one believes that the Germans were on their last legs in late 44, it takes an arrogant commander to launch an airborne attack in less than a week of planning when you don't even have the required number of transports.