... allow me to play devil's advocate.
I don't think we can dismiss a work with a John Oliver-esque "come on people its [year/genre/other indicator]". If we use that logic we can deny Romeo and Juliet as being a great romance (its teen angst with a ludicrously avoidable death scene) Hamlet as being a tragedy (first estate problems) or even the Iliad (our hero is a rapist berserker, and I am supposed to care if he lives or dies?). So lets dispose of that argument by saying "come on people its 2021, gangster films can be high art now"
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The story is horrible, but if its told well any story can be dramatic, that is to say the vehicle of good acting performances. It definitely satisfies a number of dramatic appetites, it has a massive star in Brando, a hunk in Caan, a new face in Pacino, a sweetie in Keaton so its actually a satisfying Hollywood blockbuster (it also has exotic locales! violence! sex is off screen!).
It has very interesting character development, why would a war hero become a crime boss? Other films have "honour among thieves" as a theme, but GF (as mentioned above) goes deep into the role of family and the Sicilian code as a source of loyalty and cohesion. Yes its voyeuristic, like a gratuitous native dance scene in an Indiana Jones movie ("look at these weird foreigners and their ways" "gross, a fish in a vest!") but its also presented as a working system, with real emotional consequences and political ramifications. "Look how they massacred my boi" is quite a sad moment, and its a twist because we, like the undertaker, know Vito as fearsome rather than human, and we're not sure WTF is going on until he breaks down.
Its a relevant drama too: crime syndicates have some influence in the US (I feel like Keaton is a nod to Jacquline Bouvuier marrying into the rotten Kennedy mob) and while the crime machine is background (the movie is moslty about the turf war, rather than how they work the turf) and most people know where they can place an illegal bet or visit a brothel.
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I think God Father does pass the test of being "Good Drama" on many levels. The acting satisfies a number or audiences. You want to see Hollywood stars being themselves are using art to transform themselves? Check. Do they dazzle you and make you want to watch them? Check. Is the story interesting both as entertainment, or for deeper reflection, or for escapism, or social relevance (both directly and metaphorically)? Check.
It passes the basic test that a great majority of people will find it watchable and satisfying, and you can enjoy it for many many aspects and elements. In terms of "art" I think the artists do what they wanted to do, and show great skill and good taste.