The northern part of Italy is the core industrial area, while the south is the less important agricultural area.
This means that if the northern part of Italy is captured, based on the way Italy is currently handling things, there is a high possibility that they will surrender.
Fortunately, the Austro-Hungarian Empire has lost most of its main force on the Eastern Front. Otherwise, Italy might become the slowest country to join the war and the quickest to surrender.
Of course, the current situation in Italy is not much better. Before the start of the campaign, because of the Austro-Hungarian Empire's defeat on the Eastern Front, the Italians were still dreaming of seizing more land, even occupying the whole of Albania.
But now, as the Italians fight, they are surprised to find that, not to mention expanding abroad, their own borderlines are already in crisis.