The only reason Churchill didn't care for the Italian government was their proven track record of NOT honoring their treaty committments, such as when they decided to abandon the the Triple Alliance, and join the western allies in battle against their former allies. He didn't denigerate their fighting men, but he did feel that they had a record of fickle "flip-flopping" for their own gain. He was pretty sure that they would do the same to the Axis, and they did. With friends like that who needs enemies?
Consider a different Dragoon, either a landing on the NW coast of Italy say between Genoa to La Spezia or on the Adriatic coast between Rimini and Venice. The object being to trap the German forces in Italy. Then the French/Italian and German/Italian alps work in the Allies favor. A German Army group could be captured and the north Balkans/Southern Reich threatened. The Allies do not have to attack these areas, just their presence would compell Hitler to shift troops he dosn't have to forstall any threat. Airbases could be set up in Northern Italy to strike at the southern Reich to further squeeze Germany. The actual Dragoon failed to bag any significant German forces, only force them to retreat which they would have to do in any event.
why the fuss? Anvil/Dragoon was one of the most successful operations the Western Allies put into action. Lots of territory liberated, negligable losses....it wasn't called the "Champaigne Campaign" for nothing!
Italy..the muddy campaign..some would contend could have used the L/C Churchill shouts loud about this and divergence of manpower issues..some I say... To do Dragoonand then advocate going into Italy to someof us sounds bizzare.
Keep in mind that the ports Captured in Southern France, particularly Marseilles, provided a full 1/3rd of all supplies used in the battles in northern France. By not moving north and linking up, an already strained logistical system would have been even worse.
What would be the point? Remember the Dragoon forces, three American divisions for the initial landing, followed up by five French, were pulled out of Italy just after the breakout and capture of Rome, while Kesselring's forces were falling back to the Gothic Line. Advocates of the Italian campaign, of which I am not one, cite this easing up of the pressure as a crucial mistake. If we wanted to use those divisions to fight through a mountain range into the northern Italian plains, just leave them where they are. There was another discussion on this a couple of months ago.