I think it is primarily the trust issue. Remember, in Iron Man II, Fury makes fun of the idea of Rhodey actually taking the armor. Stark allowed it to happen. In the comics, Rhodey took Stark's place as Iron Man at times. I believe that was before he got the War Machine armor.
I get what you are saying regarding the other Avengers, but why not suits more like what he made for Spider-Man? That was created to allow the wearer to take advantage of his superior agility. In both the comics and the movies, that was played as Stark seeing himself as a mentor to Peter Parker rather than considering them to be equals. That makes more sense in the movies, with Parker still being a high school student. In the comics, Parker was an adult and he had been Spider-Man for years when Stark made the Iron Spider armor.
I'm not sure if you read Civil War in the comics. I read New Avengers, which first brought Wolverine and Spider-Man into the Avengers, through Civil War, so that colors my perspective on the relationship between Stark and Parker.