The question is a faulty premise. The war in Italy isn’t forgotten. Most people who follow WWII know of the Italian campaign, but they don’t really pay attention to it because it is closer to what happened in WWI, it lacks big personalities and narratives, and because of simple bad timing. This means it isn’t really a forgotten front as much as an ignored one. At least in the US, other fronts - particularly CBI (China Burma India) - if they are thought of at all, are remembered for logistical issues (The Hump in CBI, the mountains in New Gunuea) or weather (Aleutians). The invasion of Southern France is rarely even mentioned. They are truly the forgotten fronts of WWII.

There are four main issues with why the Italian campaign is overshadowed. First, it lacks a good narrative. Second, it is not a battle of maneuver, but one of slow grinding forward, with a couple poor leaps forward. Third, its main high point - the capture of Rome - is overshadowed by D-Day and isn’t the climax of the war/campaign that it should be. Fourth, it lacks the “personalities” about which stories are told.

The Italian campaign was about opening a second front to relieve the pressure on the Soviet Union. It was not designed (nor geographically likely) to resulting in a defeat of Germany. Instead, it was a secondary theater, but at the time it began, it was the only “show” in town.

Depending on how you define it, the Italian campaign begins either with the invasion of Sicily in July 1943, or when the 8th Army landed near the “toe” on September 3, 1943. The Sicilian invasion, has an ambiguous result. It is successful in that the Allies captured the territory. It was not successful in that the majority of the Axis (primarily German) troops escaped. The Allied high command decided to use it as a test run for the cross-channel invasion that “everyone” knew was coming at some time. As a result, it was a good early dress rehearsal for the ultimate invasion of Continental Europe (i.e. France), and the Allies learned a lot that would be put into use later.

Once Sicily was captured, the Allies moved on to southern Italy. The Armistice signed on September 3, 1943 - the same day as the invasion - shifted the narrative from “taking the fight to the enemy” to... well... something less. The shift in allegiance muddies the waters, as one day its enemy territory, filled with enemy civilians, to people whose attitudes haven’t changed merely because a piece of paper was signed, and are more war weary than anything else.

The initial invasion was relatively easy, as most of the German troops had withdrawn to more defensible positions further north. The Salerno attack was hard fought, because that was the area where many of the German Troops were withdrawing through. This leads to point two - it was not a battle of maneuver, but a grinding slog reminiscent of WWI.

Southern Italy is basically “flat.” Central Italy is very mountainous, with narrow coastal plains. This strongly favors the defense. So, for the early period, the Allies advanced rapidly, and then they hit central Italy, and stopped, and wound up with something similar to the trench warfare of WWI. To advance, the Allies had to become the “Bad Guys” and destroy everything in their path. Priceless historical buildings and locations - most notably Monte Cassino, but many other places as well - were pounded into rubble because they were part of the German defensive lines, famously the Winter Line and the Gustav Line.

To get around this, the Allies made a number of landings, most famously at Anzio near Rome. Anzio is close enough to Rome where advance forces could have reached Rome on the day of the landing. But General Lucas acted far too conservatively, and was out-generaled by Kesselring who effectively bottled up the Allies. Instead of being a dramatic breakthrough that caused the enemy to retreat or be cut off, as MacArthur would do 6 years later at Inchon, the Allies were bottled up in their beachhead, and it took five months, and a change of leadership, to move from being a thorn in German’s side, to a force capable of advancing on Rome.

The climax of the story of the invasion of Italy should have been the capture of Rome. Historically, taking the enemy’s capital is the end of the story. Therefore, following historical trends, when Rome was captured, Italy should have fallen. It didn’t. The Germans simply withdrew further north into another mountainous area and set up the Gothic Line. Fighting in Northern Italy continued until after Germany surrendered.

On May 23, 1944, the Allies began Operation Diadem, which was the Anzio breakout. 12 days later, on June 4, 1944, the advance troops entered Rome and, because the Pope had declared it an open city, and Hitler, fearing another Stalingrad ordered Kesselring to not defend Rome, it was deemed “liberated.”

It took a day for the news of the liberation of Rome to reach the US. So, on June 5, 1944, the liberation of Rome was declared. This monumental achievement was quickly overshadowed by the opening of the main theater in the European Theater of War. In this respect, it was simply bad timing. From that point on, other than a few sporadic incidents in the Pacific Theater, the front page, above the fold news was the ground war in Northern Europe. Everything else was relegated to second level status.

Had Rome been captured earlier, or had Overlord occurred weeks later, it would have had more time to “stick” in the memory. In this, the memory of the Italian campaign simply was the victim of bad timing.

Fourth, the Italian campaign lacks “big” personalities to drive stories. The Pacific Theater, had larger than life personalities such as MacArthur, Halsey, and Nimitz on the American side, and Tojo and Yamamato on the Japanese side. The North African Campaign and the Northern European Campaign had larger than life personalities such as Churchill, Hitler, Rommel, Montgomery, Patton, Bradley, and Eisenhower. In comparison, the Italian Campaign, particularly once Patton was forced out, lacked those kinds of personalities. Mussolini is looked at as more of a comedic/incompetent figure. Mark Clark and Lucian Truscott are above adequate generals, but they are lacking in the kind of “big” personality for telling good stories. The Italians are also not good "villains" for narratives. The Nazis are the quintessential "Bad Guys" while the Japanese soldiers attitudes of suicidal sacrifice - whether as Kamikazes or in "Banzai Charges" makes them "alien" (there are also a strong racist overtones that drive much of the early story telling). But in the eyes of many Americans, the Italians are the "Pizza and Pasta people", not "Bad Guys."

Despite this the Italian campaign is depicted in media, but most of it is part of a larger narrative. For example, the movie Patton (1970) has significant portions take place during the Sicilian campaign. The Liberator, which was recently released on Netflix, also spends significant time in the Italian campaign sandwiched between the Northern African Campaign and the Invasion of Continental Europe through southern France.

There are many history books that cover part or all of the Italian Campaign. “The Day of Battle” by Rick Atkinson is one of the best.

The book Catch-22 (and I think the movie as well, but I’ve never seen it) is set in the Italian campaign.

In addition to “Patton” and “The Liberator” Some American made films set in the Italian campaign - in part or in whole, include “Tuskegee Airmen” (1995) and “Red Tails” (2012), “The Big Red One” (1980), and “What did you do in the war, Daddy?” (1966). Some of the films set adjacent to the Italian campaign are “Captain Corelli’s Mandolin”(2001) and “The Good War” (2002).

Some of the media references, such as Pink Floyd’s “When the Dragons Break Free” are veiled (Roger Water’s father was killed at Anzio).

So, the premise that the Italian Campaign is "Forgotten" and not depicted in the media is simply incorrect. But it certainly is overshadowed.