Well my knowledge of Italian infrastructures is probably even lower. However, here's a question: Couldn't allied vessels have embarked from north african ports (maybe also Calgiari) and then sail south of Sardinia, as far to the north-west from Axis-controlled Sicily as possible, for this hypothetical invasion of central Italy following a success in Sardinia ?
In this scenario, is not even necessary to take Sardinia. This island isn't really the Malta of Fascism, it's basically a rock that could indeed serve as a giant ship.
But the so-called "USS Corsica" already plays this role, at a lesser cost : the corsican resistants, furthermore the demotivated Italian Army, quickly managed to beat the Germans. I agree that a still axis-tied Italian Army could make the things harder, but nothing comparable to an invasion of Sardinia.
Even with a allied-invaded Sardinia, it could only play the role of a aerial base, except and unlikely for some secondary sea operations.
The operation that you describe seems to me a bit unlikely, as the western Italian coast, at least on my little knowledge, are less interesting and usable for a massive landing.
Weren't most german formations, despite allied deceptions, nonetheless located on Sicily (Herman Goring divison etc)? And following Sicily, weren't most german divisions either south around Naples or north under the command of Rommel ?
I think fast would be the last word I would use to describe Allied progress in Italy.
A successful landing near Rome might mean the Italian HQ survives, meaning that maybe they can organize some sort of defense against their former allies, now enemies, the Germans. There were, I think, quite a number of Italian divisions around Rome. Properly motivated, those could prove pretty useful in the early stages. Rhodes (and thus the Dodecanese) might go the other way as well.
I doubt that a landing at Rome would make the Italian so quick to switch their alliance. Invading the capital would maybe make the king and HQ more quick to switch, but they will loose as much credibility and legitimacy as Leopold of Belgium. In the better case, you'll have a greater and more powerful RSI.
The problem with Sardinia is the general infrastructure very few and not very big for an idea in the 60/70's Albania were described as 'Sardinia with communism'.
And probably the 60/70 have more numerous and better infrastructures than Sardinia in the same time, at least only for trying to replace the no-more aid and trade with USSR.
No a WWII Sardinia could be a aerial base, maybe a secondary sea warfare base too, but i wouldn't count too much on it. I wonder if it would be worthy to occup all the island or only the coast even in these cases.