Top ten American composers/songwriters

History of popular songs yes. History of composers and songwriters, a footnote.
Carol King has been suggested. Not sure why so few women composers/songwriters. Plenty of feminine involvement in classical performance. I don't think we feel threatened any longer. Would be a great thread to explore. 

The BEST one is Samuel Barber !

And coming from Schubert completely makes sense. It was between Barber and Copland. Copland more American imho.

Was Jim Morrison not mentioned?

Also, was the OP speaking of all genres or just rock/pop? If all, then maybe top 10 for each of the major genres: jazz, blues, pop, rock, classical...and each of these have distinctive sub groups. 

All genres. I would consider Morrison more on the performer side ie. Elvis, Sinatra, Armstrong.