I would more consider him a Shakespeare of American Cinema rather then a Homer. Shakespeare was a prolific playwright (and a poet) who wrote plays about varied subjects and situations across the World of, some of his plays are of legendary status, and others not so great (same is true of Spielberg’s movies). Shakespeare’s plays (just like Spielberg) are also grounded in history and fiction rather then folk art and local legends and mythology. Also Spielberg is rather keen on adopting other people’s work to the big screen, which is a bit disqualifying* in this regard.

If you compare Jim Jarmusch who writes about epic road trips of regular people across the country, prisoners on the run from the law seeking the American dream, Vampires, Samurai hit-man in New York, then you start seeing how he reflects on American folk culture and mythology in his movies grounded in stories about American people (ditto Coen Brothers) much like Homer’s work on ancient Greek legends and myths grounded in stories about Greek society at the time.

What I am saying is that while Spielberg (just like Shakespeare) is a prolific director that has left us with many masterpieces (and other not-so-good pieces) he has not captured American legends, American mythology, nor American folk stories in ways Homer captured the Greek legends, mythology and folk stories. Both Jim Jarmusch and the Coen Brothers however have done so masterfully.

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*: I know Woody Guthrie also played covers and collected folk music and redemption songs, but that is a bit different then adopting an already successful and widely known book into another format (ditto Homer).