You’ve got to include Henry Mancini...
And Lalo Schifrin.
Mancini didn't write that many TV show themes because the ones he did write quickly got him all the movie work he wanted.
He was writing for movies from the early 50s, as a contract composer for Universal Studios. He composed music for The Creature From The Black Lagoon, among other pictures.
But it was the theme to the TV show Peter Gunn that boosted his career to a new level.
In an interview he recorded in London, he was asked how his life changed after Peter Gunn. He answered "after Peter Gunn, my job went from 9-to-5 to 24-7." Pretty cool guy.
He also said (in that interview): "Baby Elephant Walk put my baby elephants through college."