Do you have an original death certificate? What death location and what location of the certificate is on it?
Do you have information about his burial location (not "just" tombstone).
Do you already know if he was naturalized in the US or only applied for?
But anyway, as others stated, dual citizenship is a thing. And even without Italian citizenship, you can travel there as a tourist.
My great grandparents migrated from Italy to Canada around 1910. I found sources that my great grandfather travelled from Italy to Canada in February 1906 (with his cousin), March 1906, June 1911 and March 1924 (in 1924 he did not entered the ship). My great grandmother arrived in March 1913 with her 1 year old son and her sister-in-law. They were back in Italy when their second child was born in 1922. My grandmother told me that her mother didn't feel well in Canada, so they returned to Italy.
I saw similar stories for the same village but with the US, where some distant relatives travelled multiple times between those countries. Yes, it was a long journey and very expensive, but then they had not many options to keep contact with their relatives and friends (many were illiterate, villages had no telephone yet) and why should they have missed them less than we would do today. Also, the climate might have been different than they were used to and maybe the job situation was not as good as they were hoping.
I don't know if this also happens to migrants that far away, but for Switzerland and Germany there were and are quite many migrants (from Italy, Spain, maybe others) who return to their country when they retire. Some think their whole life that they will return after retirement, they save money, maybe keep a house in their country, but when they are old, they don't have many relatives left and their children live a good life in the new country, so they don't return in the end.
Edit for typo.