The Italian front could not put pressure on Germany the way an invasion of France could. The reason was the Alps. If you were am Allied general, planning for an invasion of Germany from Italy, you will quickly see only two even remotely realistic routes, going around either side of the Alps. The bigger problem is that both of these places are essentially choke points. It was not impossible, but very unlikely, and both the Germans and Western powers knew it.

As I'm sure you know already, the invasion of Italy prompted Hitler to withdraw from the Kursk offensive. While the Russians likely could not explicitly link the two, the effect on the eastern front was noticeable. However, Stalin was still not happy about it. He viewed it as stalling by the Western powers while Soviets were dying by the millions.

While it is true the Italian campaign is pretty much ignored nowadays, the second front in the context of the time, and as the Russians demanded it, was a second front directly against Germany in Europe, opposite the East front. The Italian campaign was, at least initially, against another axis power - Italy and seen more like a indirect underbelly attack, like the campaigns in Africa. Hence the France invasion is seen as the 'second front' in popular narrative.

Ps: for those interested in the Italian campaign I recommend Rick Atkinson - the day of battle. Awesome book

I had another question come to mind. Italy was used as a base for bombing. Did the US & Brits have well coordinated bombing campaigns in support of Russian ground troops? Was the relationship with the Russians that close?

A big reason why the Italian campaign was not considered the second front was because it was merely an extension of Operation Torch.

In my opinion Operation Torch was not a serious attempt to getting closer to ending the war. Churchill believed that it would allow the British to increase their influence on the Mediterranean region after the war. Roosevelt used it as a cheap way to win popularity points for the 1942 elections by engaging the Axis power in Europe even if it was largely against the lowly Italian army and a small detachment of Germans.

There was no foreseeable route from Rome to Berlin due to the Alps which limited the goals of the Italian campaign. Germany knew this and committed fewer troops to the defense of Italy. However, there still was an effect on the eastern front.

I believe most would agree that the Mediterranean theater lengthened the war as it stretched the Allies out more than it did the Axis powers. The strain on Allied shipping was made worse by having to supply troops in the the Mediterranean. Those troops in the Mediterranean theater also could not be brought to bear in France, thus delaying D-Day.

To be certain, the Italian technically opened a second front on the European mainland, it was still not enough by the Soviets. They perceived (rightly so) that Stalingrad was the turning point in Europe which concluded 6 months before any western Allies stepped foot in Italy.

The Italian campaign did not divert enough German resources from the eastern front for the Soviet's liking which was used in their Cold War propaganda against the western Allies. Plus, with the advantages of hindsight, we know that the main western Ally offensive against Germany started in Normandy not Salerno.