1. Was the US Army unready? Sure. But we weren't the only ones that would have been involved. The Brits - who had a larger contingent of soldiers in uniform in Europe than we did before D-Day - were not unready, and were well and effectively led. And frankly speaking, we would have had not only air superiority but also a relatively safe supply chain...and in war, superiority in air and logistics can go a very long way to more than making up for a difference in quality of the troops.
2. Churchill did not have 'more to gain' by fighting in the Med, unless by 'more to gain' one is referring to "fighting the Nazis in such a way that we look like we're doing something really important while in reality we're attacking the one front that did not present an existential threat to Hitler, thus enabling him to continue the fight against the Soviets". As I pointed out in the article, by late 1942, the Afrika Korps no longer presented a threat to the all-important Suez Canal and the other British strategic assets in the Med. Yes, Churchill referred to the Balkans as the "soft underbelly" of Europe...but by then, we could already see that the Wehrmacht was in retreat in the Ukraine SSR and the Soviets would soon be threatening the oil fields in Romania, thus obviating any real benefit to us attacking there.
3. In 1943, the Luftwaffe was fully engaged on the Eastern Front. In fact, the Brits' bombing campaign against Germany proper had already begun in late 1942. The Nazis were already playing defense - over the Channel and northern France, the Brits already had air superiority.