Few things woulc have benefitted Hitler more than having his entire southern flank neutral and secure. No doubt Churchill would still be concocting schemes to involve Turkey or Yugoslavia in the war, but Hitler could remind them, perfectly honestly and in conformance with international law (something of a novelty for him) that neutral countries cannot allow their territory to be used by belligerents and that such action would entitle Germany to act to defend herself. While I'm not bashing the Italians, their contribution to the Eastern Front hardly compares to the value of the German troops, armor, vehicles, combat and transport aircraft, etc. that would not be tied up in the Mediterranean. Nor does Italy's neutrality give Romania any less reason to side with Germany against the ongoing threat of the USSR. Without an active front in the Mediterranean, Britain and Churchill would have few serious options for carrying on the war, though I expect they could hold out themselves almost indefinitely. The whole might seem a bit pointless. The naval assets - aircraft carriers, destroyers - not tied up in the Med could significantly aid the battle of the Atlantic. They wouldn't be throwing together a Force Z at the last moment to try to deter the Japanese; rather as tensions grew they could build up land, sea, and air forces in the Far East. There would be little reason to retain the Anzacs or Indians in the Middle East. The "lifeline of Empire" through the Mediterranean would be open.