IMO it was not a question of Sardinia after North Africa, but what after Sicily. Reality is that Sicily, should come first - because of the terrain makes airfields possible; with Sardinia its too mountainous to house Allied air power.
But then politics came into play - trying to help the Italians defect, though some may argue not very well.
From Sardinia, comes Corsica, and having that - threatens the Germans with a landing on the South of France, or the coast of Italy - higher up than Salerno.
Churchill thought that Italy was the 'soft underbelly of the Axis', in a way he was right - unfortunately this was only militarily. Italy, geographically was anything but soft - especially the west. It only IMO had one target worth going for - and that was the Foggia airfield complex. Once that was attained (with a defensible northerly perimeter), the threat could be a landing on the north Yugoslav coast!
Hence with this combination, German forces will have greater dispersion.