As a starting point, Northern Italy is surrounded by mountain ranges, to both the north (border with Austria) and the west (border with Vichy France). If it looked like the Allies were getting close to the north and could potentially enter France that way, I'd imagine German troops would be redirected to help reinforce it, and seeing as how mountainous that area is, the fighting probably wouldn't be easy. Not to mention the logistics of getting any armour through.

As for D-Day itself, as had been used in Operation Mincemeat before the invasion of Sicily, Operation Fortitude had succeeded in convincing the Germans that a much larger force would be heading for Calais, so much of the German defences were redirected to reinforce it. After all, they'd seen plenty of tanks, planes and other vehicles during bombing raids over Britain, and Calais made the most sense to attack because it was the closest point to Britain. There would certainly be a significant loss, as by this point defending against an opposed landing wasn't too difficult compared to how it used to be, but with that loss the Allies would regain a foothold in the Western Theatre. But it is true to say that the Germans knew they were coming, they just expected an even larger force at Calais and so didn't worry too much about Normandy.

The D-Day invasion was politically necessary, above all. The Western Allies had obligations to the Free French and also to the Soviet Union to put pressure on the Axis and to liberate France, and moreover, there was significant pressure from both the American Chiefs of Staff and the general public to launch a large scale intervention - in the former's case, they had championed an operation on the continent, 'Roundup', since 1942, but had been dissuaded from this course by the British, and although Grigg argued that it was feasible, the general consensus in the scholarly community is that it was the sensible course of action.

As for invading a fortified coast, the Allies by now had considerable experience of it, from both failed expeditions, Dieppe in particular, and numerous successful ones, in Madagascar, North Africa, and Sicily, and had honed techniques for beach landings, not least of which was the design of adequate landing craft, but also sophisticated intelligence and misdirection operations.

Would the Allies have been able to re-take the continent via Italy? I am loathe to dabble in counter-factual history but I would be inclined to say no. As the other respondent to your question has highlighted, Italy is a mountainous country with relative limited space for manoeuvre, which would prevent the amassing of vast forces, and aided German defensive operations. As a result, the vast Allied materiel and manpower superiorities would be comparatively less useful and the going would be far slower; the Allies knew this of course, and the plan of invading Italy in the first place had largely been useful on a grand strategic level - First, it took pressure off the Russians by opening a second front. Second, it tied German forces down to an area they could not supply as easily - Alanbrooke correctly identified that Germany's North/South supply lines were far weaker than their East/West transit links. Third, it took Italy out of the war, thereby denuding the Axis of materiel and basing, as well as the goodwill of the populace. Italy was, despite Churchill's best insistence, largely a sideshow - a place to put pressure on the Germans, politically useful, but a diversion from the main thrust.

As a result, I would argue D-Day was not only politically, but strategically necessary for the Western Allies to liberate as much of Europe as they did, whilst Italy, though a vital part of Allied warmaking, was never a path to victory.

Grigg, 1943: The Victory That Never Was (1980) - this text is highly controversial, and is strongly disagree with by many academics, but nevertheless interesting

Jones, Britain, The United States and the Mediterranean War, 1942-44, (1996)

Major-General I. S. O. Playfair, History of the Second World War: Mediterranean and the Middle East, vol.4: The Destruction of the Axis Forces in Africa, (1966)