"I once made the mistake of asking Quentin why he liked Rio Bravo so much. He just went on and on, opening with, 'You know ... I didn't have a father.' I thought, 'Uh-oh'" -- Elmore Leonard, here.
If Leonard can't quite see why Rio Bravo is such a big deal to some viewers (particularly to boys without fathers, it would seem), neither can I. It strikes me as a by-the-numbers Howard Hawks' effort: introduce hero in a scene that establishes his predicament, move to scene confronting hero's moral vulnerability, inject intermission scene with comic dialog between cronies, interrupt laughs with scene where hero proves himself capable. Lather, rinse, repeat.
As for the performances, John Wayne is interesting to watch only because he seems to be improvising his mood for each set-piece. He's uncharacteristically light in this film -- in one scene he sternly admonishes his younger deputies, in another he literally skips across the floor on his toes after giving "Stumpy" (Walter Brennan, chewing the scenery with a brio that defies send-up) a smooch on the noggin. Hawks doesn't give Wayne anything to really brood over, so Wayne has no center of gravity (unlike The Searchers, The Man Who Shot Liberty Valance, True Grit or even The Shootist). Angie Dickinson begins with some substance as a woman dealing with a reputation that's been established for her by someone else, but is reduced to a drunken flush of girlish vapors. Dean Martin declared this to be his toughest role ever, a statement which requires about as much consideration from the viewer as Martin gave to any of his other roles. Someone else was in that movie too, another singer-type* ....
Still, I'm the guy who likes Gidget, so if someone like Charles Taylor stands up and says says, "If I were asked to choose a film that would justify the idea of America, it would be Rio Bravo," I'm all ears. Via ALD.
Post-Script: were I to choose an over-the-top Western that embodies the idea of America, it would probably be Vera Cruz. When I saw it as a kid, I tried to grin like Burt Lancaster for weeks afterward.