>>Doesn't our stage musical tradition comes from a blending of German orchestral music and Anglo-Irish lyricism?

Short answer is, "No, it doesn't"--the most immediate reason being that neither of those are theatrical traditions--Sigmund Romberg, Victor Herbert, and Franz Lehar were big names in the relatively early stages of American Musical Theatre, two were born in Austria-Hungary, one in Dublin, but all learned their craft in Vienna, and, though the father of American Musical Theatre is considered to be George M. Cohan, who was nothing, if not a Yankee Doodle Dandy--

The point being that musical theatre and doo wop were products of a place and time and had more to do with that than any remote roots--