Bob Dylan.
Lennon & McCartney were good, too.
Good choice
Also: Amy Winehouse and Kurt Cobain. Ah well, the famous 27 Club
This looks really similar to my top 10 over rated musicians of all time. The Beatles sucked as a boy band unless you were a teen girl at that time, then you get into the Beatles acid trip days and you would have to be as high as they were to enjoy that. Dylan pushed some boundaries like bringing an electric guitar to a folk concert but much of his early days was impressing freaks in the UK with his poetry. He knew he was an awful singer, but his lyrics are highly over rated and the music put with the lyrics weren't very good either. Winehouse and Cobain are honored because they overdosed young, but art is in the eye of the beholder.
So best songwriter should include both lyrics and instrumentals, many songs are a collaboration of a few artists and then it's up to the producers to put that music in front of the population. Much of our music is only "great" because it's been pushed upon us and played over and over to get into our heads, some of the greatest music has not had these privileges and so it is over looked. So my question is are we looking for the best lyrics here? Or the best instrumental, or just songs that make us feel good? What works for one generation doesn't always fit for another. Ed Sheeran and Taylor Swift are both examples of currently active song writers that are bringing meaning to what is going on today. Some think Eminem is one of the best songwriters of all time while other rappers have no respect for him. Prince has contributed to many performers and his music and lyrics were pretty good, but he had a very strange relation with the press and public so some many people over look him. Should music make you laugh? Or cry? Or make you want to dance? The styles of music are much too great to say there is one GOAT of anything whether it be songwriters, songs, or artists.