One of the great controversies of WWII was Churchill advocating for the cancellation of Anvil, the invasion of Southern France and eventual link-up with Eisenhower, in favor of leaving the troops in Italy under Alexander to fight through the mountains and Gothic Line into the Po Valley, over to Trieste, up the Gap and somehow beat the Russians to Vienna and Budapest. When Roosevelt and Marshall turned him down, with Brooke's support, he later proposed a landing near Trieste to do the same operation.
The problems were manifold. The Germans had proven in Italy to be masters of defensive warfare in the mountains. The roads and railroads were thin if not poor. Inside the Gap there was only room for two divisions to maneuver, so "shooting" the Gap was not feasible. North of Ljubljana there were more mountains and passes to force. And if the Allies pulled it off, of what value was Vienna compared to the Ruhr and a path to Central Germany and Berlin?
Churchill was a great wartime leader, but the war plans were better left to others.
Well put. After Sicily, British troops in Italy had to be put under US command which was better able to get them to fight, and even that was of limited success. Brooke knew that US support would be essential for continued fighting in Italy -- some of if not the worst terrain for combat in the entire war -- and after the southern objectives were in hand (13 airfields, putting occupied e Europe's oilfields and factories in range of British bombers) there was no further point to fighting in Italy. Churchill was unmatched in his speeches, but was always looking beyond the war, how best to position the UK at as little cost as possible, as it devolved its empire; that he was a sneaky little **** was shown during a wartime "Big Three" conference, when he slipped Stalin a note proposing a percentage division of influence over each of the eastern European nations after liberation (it was pointed out that it would be like trying to keep a woman half-pregnant), and Stalin mock-innocently brought it up in front of FDR, knowing full well that Churchill had never told him about it.