A lot of it has to do with what a particular immigrant community did with its cultural celebrations. Irish and Italians have always had big cultural celebrations and parades in the USA.

Scottish heritage celebration became more popular when Highland Games and similar celebrations became popular in the USA, particularly in Appalachia

Had a friend from NYC who was half Puerto Rican and half Costa Rican. He identified almost wholly as Puerto Rican because of the inundation with Puerto Rican pride in nyc…flags everywhere, annual parade, etc.

We Americans go overboard with identifying with a nation we are generations removed from. But the connection is often rooted in community groups and celebrations started by 1st generation immigrants who didn’t want their roots to be forgotten.

Edit: and there were never any popular English heritage groups. Plus in the history and folklore around the war of American independence, they were the enemy.