Top ten American composers/songwriters

Robert Ellsworth Pollard at the top of the list. 

Some good candidates already mentioned. Also:

Samuel Barber
Walter Piston
Howard Hanson
John Adams
Elliot Carter
Phillip Glass (reluctantly and depending on how one defines “top” 🤔)

In Jazz and popular music:

Billy Strayhorn
Wayne Shorter
Benny Golson
Thelonious Monk
Cole Porter
Ervin Berlin
Hoagy Carmichael
Jerome Kern
Stephen Sondheim
Oscar Hammerstein
Stevie Wonder

Hank Williams
Chuck Berry
Bob Dylan
John Fogerty
Paul Simon
Stevie Wonder
Carole King
Randy Newman
Bruce Springsteen
Tom Petty

That's my list for popular music.  For me, Randy Newman comes in just before James Taylor.  Joni Mitchell and Neil Young are ineligible, since they were both born in Canada.  I would have to make another list for jazz (Monk, Ellington, Shorter, etc.), and Broadway (Gershwin, Rogers and Hammerstein, Stephen Sondheim, etc.). 

Stephen Foster
Born 1826 Pennsylvania