I've heard a lot of synthetic trumpet sounds on various popular songs. None sound much like a trumpet, so I am skeptical it is a "simple to model" problem.

(I played a trumpet as a kid, so I suppose my ear for it is more discerning than most. My talent proved elusive, but the lasting value was I can appreciate how incredibly good Herb Alpert was. He could play like Fred Astaire could dance and Ernst Udet could fly.)