[spoiler for Fort Apache later in this post]
First of all, Wayne was a fine actor. Granted, he didn’t often stretch his range, but within that range, he was considerably better than many people grant him.
Wayne was a movie actor, and his talent wasn’t for making great orations (which is what many people mistake for great acting talent), but in the small subtle things that people don’t think of when they mention Great Acting.
There is a moment in Fort Apache that illustrates this perfectly. In the film, Henry Fonda plays a glory-loving military commander who ends up having his men massacred in a parallel to Custer’s last stand. Wayne is his second in command, who has sympathies with the Indians and has all the reason to hate Fonda because Wayne gave his word to the Apaches, and Fonda went back on it. But Fonda, like Custer, became a hero back east.
Afterwards, Wayne is commander and a reporter is talking to him. A painting had been made of the battle, showing Fonda dying gloriously. The reporter asks Wayne “Did the painting get it right?” There is a pause, and a close-up of Wayne.
In that short close-up (no more than five seconds), you can see Wayne thinking, considering all the aspects, and making a decision. He stands and says “That’s exactly the way it happened” because he does not want the deaths of the men to seem as futile and stupid as they really were. (It’s also a precursor to that famous line in “Liberty Valance”: “When the fact becomes legend, print the legend.”)
Few other actors could portray the ambivalance of the character, the ideas that flickered through his head.
Wayne did first-class work there, in “She Wore A Yellow Ribbon” (he was bothered he didn’t get an Oscar nomination for that, and he was right), “The Searchers,” “True Grit,” “The Shootist,” and “Stagecoach,” to name a few.