Patton, for all his bluster, was a serious student of ancient military history. What he saw developing was something like what happened in the second Punic War, and what Rome had done about it was to hop the periphery of the island clockwise, south to north. Once you hit Messina, Italy is a short boat-ride away. We took 100,000 Italian POWs because we had them encircled.
There were other issue surrounding that particular attack at that particular time. Stalin had been (rightfully, in my opinion) demanding a second front to relieve pressure on his own. It was well-known that a channel crossing would take assets we did not have in place and technology that didn't even exist yet. Both the Brits and the U.S. were deployed to North Africa at that point, also over ground that the Carthaginians and the Romans had fought. Sicily was an obvious stepping stone.
That was not lost on the Germans, themselves students of ancient warfare. It partially explains, I suspect, why they managed to leave the Italians holding the bag (it was their own territory, after all) and retreat slowly up the length of Italy. My late father followed them step for step the entire route, and his descriptions of the terrain match those of the article, sans a few expletives about managing mules through the Italian mountains.
What Churchill meant by "soft underbelly" was that the Germans didn't have defense in depth there to the degree to which they did on the Eastern front or that they still were developing at the Atlantic Wall. German planners felt that a slow retreat through Italy would buy them the requisite time, and for the most part they were correct; what happened, however, was a shortage of assets to develop a fourth front north of there once the third opened on June 6, 1944, in Normandy.
No, what he meant by, “soft underbelly,” is, it was economically in the best interest of the British Empire to occupy Sicily.
The battles between Rome and Pyrrhus were in mainland Italy. Pyrrhus did go to Sicily but he fought the Carthaginians there. Rome forced Carthage to give up Sicily entirely in the peace treaty at the end of the First Punic War. After the battle of Cannae in the Second Punic War, Syracuse revolted from Rome and had to be reduced by siege—the Carthaginians did what they could to aid the Syracusans. Other than that the Romans and Carthaginians did not fight in Sicily in the Second Punic War.