Kind of funny you specifically call out Irish-Americans, because Ireland does actually have some options for citizenship-by-descent. It’s not quite as simple as anyone with Irish ancestry can become a citizen, but it is a thing.

If you have a grandparent who was born in Ireland you’re eligible

Or if your parent was an Irish citizen at the time of your birth

So hypothetically if you have a great grandparent born in Ireland, your parent could apply for Irish citizenship, even though their parents (your grandparents) weren’t citizens and had never set foot in Ireland

And if they did that before you were born you would also be eligible

And so on down the line to your children, and their children, etc. if everyone keeps on top of it.

There’s actually a decent handful of countries with some sort of citizenship-by-descent, not a majority by a longshot, and of course every country that does offer it has different requirements and restrictions, but for some people it can potentially be a viable pathway to another citizenship.