Pierogies, eh? I used to fry those bad boys in olive oil with onions. Now, our current au pair, who is from Poland, makes them for us from scratch. I’ll try your suggestion of using them in lieu of noodles or dumplings—sounds like it has potential. (It’s going to be hard to beat those Bisquick dumplings, though—chicken stew and dumplings was one of my favorite recipes of mom since I was a little Mr. Poopiepants). 
I’ve thought of this as a Central/Eastern European thing (which would partially gel with the Jewish theory, I suppose). I always use parsnips, but I got that both from my parents (who are Polish Catholics) and from living in Hungary, where parsnips were always part of any “soup vegetable” package. Another defining flavor of Central/Eastern European chicken soup is cereraic/celery root in the place of celery stalks.
Poles do not traditionally use pierogi in soup, but ask your au pair to make “uszka” (“little ears”), which are miniature pierogi, very much like tortellini, that are used for soup. If you want to use pierogi, that’s fine, but there is a specific stuffed pasta for this in Poland, just so you know and your au pair doesn’t look at you funny. Traditionally, they are used in barszcz (brothy Polish borscht). I’ve never seen it used with chicken soup, but they would definitely work better than pierogi–they’re just a better shape and size for such an application–very much like the Italian tortellini al brodo.
And that should have been “celeriac” in my previous post.
Yeah, the broth certainly adds flavor to the pasta, and in small quantities, I agree with you.