Should they not have been more worried about problems closer to home..?
Sure they should have, but that's how things go in wartime and especially in wartime with dictators. They get a propaganda bee in their bonnet, get fixated on looking good, or looking strong and then tend to ignore more pressing concerns.
But just because Mussolini didn't do well in the end doesn't mean that propaganda and moral lifting isn't an important part of war. The Doolittle Raid on Tokyo in 1942 is a point in case, not very unsimilar to a never realized New York bombing ... as a raid judged on destruction of enemy war production means it didn't accomplish much at all. But by bombing Tokyo it inspired the US to look at things in a positive light. It was wonderful for national morale. The Doolittle Raid on Tokyo was just as much a publicity stunt as anything else ... the Italian raid though is that it was never carried out and even worse, Mussolini did not win the war.
The same would have happened with an Italian bombing of New York. Imagine the headlines around the world. Imagine the scope for movie productions ...