Most of those countries wouldn't agree with a word "liberated"
It's like the USA "liberating" Philippines from Spain, then Japan "liberating" Philippines from the USA and then the USA "liberating" Philippines from Japan
ooooh, a thread which fits my tastes perfectly!
Second, ofc OP was describing a HOI3 game mechanic real life scenario, but the real reason for that the allies were unable to invade Southern France or Northern italy direct off, was the simple fact: Supplylines. Out of three major invasions(Italian counted as one) in European Theater, one was not within close range of supplies: Operation Torch (North Africa). Now, Operation Torch is a little special. The enemies had not massively prepared defences, and was "generally" "unprepared". Now, this is not enteriely true, but to understand that, read the Wiki article, it's good. Anyways, Operation Torch succeeded because the bulk of enemy forces where in Libya/Tunisia, not Marocco/Algeria.
Compare to Sicily and Mainland Italy invasions. Sicily is just off the coast from Tunisia, and a supply ship can cross the straits during day, unload/load during night, and return next morning, from Tunis, while from Tripoli, it can take up to 24 hours, just the moving part. This is the reason why the Germans bunkered up there, and if you know about the Kesserine Pass, you also know that Rommel was wounded and moved out of country, and that Hitler didn't give reinforcements.
Now, coming to the invasions, the allied forces could not just invade from Sicily into Rome, as the closest real supply ports are around Napoli (Therefore the more common "Anzio", where the landings took place). Of course, there are ports just close to Rome, but when you are talking a invasion supply rout, you maybe heard of the floating harbours they built in Normandy? It's because we are talking large transport ships here, not some random fishing boats.
A good commander has three skillsets, in decending importance: Logistics, Logistics, Logistics (Logistics, tactical picture/strategic picture)
Edit: Liberation talk! - DR