Originally Posted by ThePowerCosmic
Cap showed he was a great leader in WW2, which Stark and probably the rest of the team already knew about. His experience wasn't seen as out of date because this was a war, and his specialty is war.
I'm reading this bolded part over and over again, but I don't really understand what you're saying except for the out of date part.
Warfare has changed, though. In his time, they didn't have stuff like close-air support, so it stands to reason that someone would have doubts about him being the best man for the job.
Not that Steve isn't, but its a valid, justified concern. And it fits thematically, as Steve has doubts about the modern world, and having someone on the team also having the opinion that he might not be the man for the job would have emphasized that.
But no, they're all believe in him, despite being a standoffish bunch. The damn Hulk listens to him. As does Thor, and what does Thor know about Captain America, or WWII, for that matter.
It makes it all look like the question "what place does Cap have in the world" is all in Steve's head.