The average American doesn't know an Ashkenazi from an alpaca.

Yes, but the average American also thinks of an Ashkenazi Jew when they think of a Jew, and has no idea that Sephardim & mizrahim even exist, even if they don't know the words for any of it.

OP's point is to refer to these people as Ashkenazi. To think of them as that, instead of (or perhaps in addition to) as Jewish.

My point is we are a long way away from that, despite how many Ashkenazi Jews live in the US.

My point being that the word "Ashkenazi" is still not understood by most people.