Is it just a numbers answer? I know that Italians immigrants outnumbered Irish immigrants during the mass migration to America in the 19th and 20th centuries; but there was still a large amount of Irish immigrants during this time. It is curious to me that Italians brought with them an extremely rich tradition that still can be found today in Italian households, the food, music, art, language, wine, are all points of pride for many Italian Americans. As an American with Irish heritage myself (both my mother’s maternal and paternal grandparents are Irish so her side of the family is 100% of Irish descent) I have not observed this to nearly the same level. The only manifestations I have seen of Irish culture are through singing folk songs at family gatherings and a love of Jameson and harp lager. The biggest difference I have noticed is the food, my mom has two recipes that have been handed down to her, one for Irish soda bread and the other for mince pie, besides that her cooking is very basic American cooking. I know I am drawing a lot from personal experience but I heard similar things from cousins and friends with similar backgrounds.
P.S. This question arose from a conversation with a friend of Italian descent. His family is constantly cooking Italian food, going to Italian markets for specialty imports like olives, salami, wine, etc. They also casually slip in Italian words into their everyday conversations, enjoy Italian classical music and have many vinyl records of it, and generally seem to be a lot more knowledgeable of their homeland. I joked to him that I don’t even think Irish markets exist , at least I’ve never seen one. Music is also different, I have never seen an Irish record or CD, but at family gatherings there is a lot of singing of traditional Irish folk songs like Danny Boy and Parting glass, but those have just been passed down orally as opposed to recorded. Religion seems to be a huge commonality, we were both raised catholic and that was a major part of our childhoods. Another thing that aroused this curiosity was the fact that technically my side of the family was closer to Irish than his was to Italian. Like I said in the OP, my mother is second generation whereas his parents are third or fourth, additionally, my mothers family is constantly taking trips to Ireland and we still have family there, so it is not from a lack of knowledge about Irish culture, it is some other reason.
This previous answer that focuses on food may be of interest:
And language:
https://old.reddit.com/r/AskHistorians/comments/bf8v7w/how_common_was_the_irish_language_in_the_us/
More can always be said and i hope you get an answer :)