Another interesting post, thanks you HH, I am enjoying the thread. Sondheim is an interesting one. Yes, as you point out he wrote the lyrics to West Side Story but had he stayed a lyricist as opposed to a lyricist composer then would he be as well known?
I get your point about Hart, perhaps only Porter approaches him for wit but both Porter and Rodgers and Hart produced musicals filled with clever songs rather than great musicals. Arguably Porter only hits a great musical with Kiss Me, Kate, and R&Hart with Pal Joey.
And again you are right about Hammerstein, maybe a second tier lyricist but his vision of the musical is central to its development.
In terms of the composers, I know anyone with an interest will know Kern but I suspect that many who know of Gershwin or Rodgers might not know of him.